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nur für ",[568,1090,1092,1113],{"className":1091},[571],[568,1093,1095],{"className":1094},[575],[577,1096,1097],{"xmlns":579},[581,1098,1099,1110],{},[584,1100,1101,1103,1106],{},[592,1102,604],{},[596,1104,1105],{},">",[1107,1108,1109],"mn",{},"0",[606,1111,1112],{"encoding":608},"x > 0",[568,1114,1116,1135],{"className":1115,"ariaHidden":614},[613],[568,1117,1119,1123,1126,1129,1132],{"className":1118},[618],[568,1120],{"className":1121,"style":1122},[622],"height:0.5782em;vertical-align:-0.0391em;",[568,1124,604],{"className":1125},[672,673],[568,1127],{"className":1128,"style":1071},[691],[568,1130,1105],{"className":1131},[1075],[568,1133],{"className":1134,"style":1071},[691],[568,1136,1138,1142],{"className":1137},[618],[568,1139],{"className":1140,"style":1141},[622],"height:0.6444em;",[568,1143,1109],{"className":1144},[672],", weil der Logarithmus nur für positive Zahlen definiert ist.",[925,1147,1148,1297,1298,1326,1327,1385],{},[568,1149,1151,1190],{"className":1150},[571],[568,1152,1154],{"className":1153},[575],[577,1155,1156],{"xmlns":579},[581,1157,1158,1187],{},[584,1159,1160,1170,1174,1180,1183,1185],{},[587,1161,1162,1168],{},[584,1163,1164,1166],{},[592,1165,594],{},[596,1167,598],{},[592,1169,601],{},[596,1171,1173],{"stretchy":1172},"false","(",[827,1175,1176,1178],{},[592,1177,601],{},[592,1179,604],{},[596,1181,1182],{"stretchy":1172},")",[596,1184,959],{},[592,1186,604],{},[606,1188,1189],{"encoding":608},"\\log_a(a^x) = x",[568,1191,1193,1288],{"className":1192,"ariaHidden":614},[613],[568,1194,1196,1200,1242,1246,1275,1279,1282,1285],{"className":1195},[618],[568,1197],{"className":1198,"style":1199},[622],"height:1em;vertical-align:-0.25em;",[568,1201,1203,1208],{"className":1202},[627],[568,1204,631,1206],{"className":1205},[627],[568,1207,635],{"style":634},[568,1209,1211],{"className":1210},[639],[568,1212,1214,1234],{"className":1213},[643,644],[568,1215,1217,1231],{"className":1216},[648],[568,1218,1220],{"className":1219,"style":653},[652],[568,1221,1222,1225],{"style":656},[568,1223],{"className":1224,"style":661},[660],[568,1226,1228],{"className":1227},[665,666,667,668],[568,1229,601],{"className":1230},[672,673,668],[568,1232,678],{"className":1233},[677],[568,1235,1237],{"className":1236},[648],[568,1238,1240],{"className":1239,"style":685},[652],[568,1241],{},[568,1243,1173],{"className":1244},[1245],"mopen",[568,1247,1249,1252],{"className":1248},[672],[568,1250,601],{"className":1251},[672,673],[568,1253,1255],{"className":1254},[639],[568,1256,1258],{"className":1257},[643],[568,1259,1261],{"className":1260},[648],[568,1262,1264],{"className":1263,"style":845},[652],[568,1265,1266,1269],{"style":866},[568,1267],{"className":1268,"style":661},[660],[568,1270,1272],{"className":1271},[665,666,667,668],[568,1273,604],{"className":1274},[672,673,668],[568,1276,1182],{"className":1277},[1278],"mclose",[568,1280],{"className":1281,"style":1071},[691],[568,1283,959],{"className":1284},[1075],[568,1286],{"className":1287,"style":1071},[691],[568,1289,1291,1294],{"className":1290},[618],[568,1292],{"className":1293,"style":722},[622],[568,1295,604],{"className":1296},[672,673]," für jedes reelle ",[568,1299,1301,1314],{"className":1300},[571],[568,1302,1304],{"className":1303},[575],[577,1305,1306],{"xmlns":579},[581,1307,1308,1312],{},[584,1309,1310],{},[592,1311,604],{},[606,1313,604],{"encoding":608},[568,1315,1317],{"className":1316,"ariaHidden":614},[613],[568,1318,1320,1323],{"className":1319},[618],[568,1321],{"className":1322,"style":722},[622],[568,1324,604],{"className":1325},[672,673],", weil ",[568,1328,1330,1347],{"className":1329},[571],[568,1331,1333],{"className":1332},[575],[577,1334,1335],{"xmlns":579},[581,1336,1337,1345],{},[584,1338,1339],{},[827,1340,1341,1343],{},[592,1342,601],{},[592,1344,604],{},[606,1346,835],{"encoding":608},[568,1348,1350],{"className":1349,"ariaHidden":614},[613],[568,1351,1353,1356],{"className":1352},[618],[568,1354],{"className":1355,"style":845},[622],[568,1357,1359,1362],{"className":1358},[672],[568,1360,601],{"className":1361},[672,673],[568,1363,1365],{"className":1364},[639],[568,1366,1368],{"className":1367},[643],[568,1369,1371],{"className":1370},[648],[568,1372,1374],{"className":1373,"style":845},[652],[568,1375,1376,1379],{"style":866},[568,1377],{"className":1378,"style":661},[660],[568,1380,1382],{"className":1381},[665,666,667,668],[568,1383,604],{"className":1384},[672,673,668]," immer positiv ist.",[564,1387,1388],{},"Man nutzt die Regeln beim Lösen von Gleichungen und beim Vereinfachen von Termen.",[559,1390,1392],{"id":1391},"beispiele","Beispiele",[568,1394,1397],{"className":1395},[1396],"katex-display",[568,1398,1400,1478],{"className":1399},[571],[568,1401,1403],{"className":1402},[575],[577,1404,1406],{"xmlns":579,"display":1405},"block",[581,1407,1408,1475],{},[584,1409,1410,1430,1432,1434,1437,1440,1451,1469,1471,1473],{},[827,1411,1412,1415],{},[1107,1413,1414],{},"5",[584,1416,1417,1427],{},[587,1418,1419,1425],{},[584,1420,1421,1423],{},[592,1422,594],{},[596,1424,598],{},[1107,1426,1414],{},[1107,1428,1429],{},"7",[596,1431,959],{},[1107,1433,1429],{},[596,1435,1436],{"separator":614},",",[691,1438],{"width":1439},"2em",[587,1441,1442,1448],{},[584,1443,1444,1446],{},[592,1445,594],{},[596,1447,598],{},[1107,1449,1450],{},"10",[584,1452,1453,1455,1467],{},[596,1454,1173],{"fence":614},[827,1456,1457,1459],{},[1107,1458,1450],{},[584,1460,1461,1464],{},[596,1462,1463],{},"−",[1107,1465,1466],{},"4",[596,1468,1182],{"fence":614},[596,1470,959],{},[596,1472,1463],{},[1107,1474,1466],{},[606,1476,1477],{"encoding":608},"5^{\\log_5 7} = 7, \\qquad \\log_{10}\\left(10^{-4}\\right) = -4",[568,1479,1481,1583,1721],{"className":1480,"ariaHidden":614},[613],[568,1482,1484,1488,1574,1577,1580],{"className":1483},[618],[568,1485],{"className":1486,"style":1487},[622],"height:0.8991em;",[568,1489,1491,1494],{"className":1490},[672],[568,1492,1414],{"className":1493},[672],[568,1495,1497],{"className":1496},[639],[568,1498,1500],{"className":1499},[643],[568,1501,1503],{"className":1502},[648],[568,1504,1506],{"className":1505,"style":1487},[652],[568,1507,1509,1512],{"style":1508},"top:-3.113em;margin-right:0.05em;",[568,1510],{"className":1511,"style":661},[660],[568,1513,1515],{"className":1514},[665,666,667,668],[568,1516,1518,1568,1571],{"className":1517},[672,668],[568,1519,1521,1533],{"className":1520},[627,668],[568,1522,1524,1527,1530],{"className":1523},[627,668],[568,1525,1013],{"className":1526},[668],[568,1528,1017],{"className":1529},[668],[568,1531,635],{"className":1532,"style":634},[668],[568,1534,1536],{"className":1535},[639],[568,1537,1539,1560],{"className":1538},[643,644],[568,1540,1542,1557],{"className":1541},[648],[568,1543,1546],{"className":1544,"style":1545},[652],"height:0.1944em;",[568,1547,1548,1551],{"style":1036},[568,1549],{"className":1550,"style":1040},[660],[568,1552,1554],{"className":1553},[665,1044,1045,668],[568,1555,1414],{"className":1556},[672,668],[568,1558,678],{"className":1559},[677],[568,1561,1563],{"className":1562},[648],[568,1564,1566],{"className":1565,"style":1058},[652],[568,1567],{},[568,1569],{"className":1570,"style":1064},[691,668],[568,1572,1429],{"className":1573},[672,668],[568,1575],{"className":1576,"style":1071},[691],[568,1578,959],{"className":1579},[1075],[568,1581],{"className":1582,"style":1071},[691],[568,1584,1586,1590,1593,1597,1601,1604,1650,1653,1712,1715,1718],{"className":1585},[618],[568,1587],{"className":1588,"style":1589},[622],"height:1.2141em;vertical-align:-0.35em;",[568,1591,1429],{"className":1592},[672],[568,1594,1436],{"className":1595},[1596],"mpunct",[568,1598],{"className":1599,"style":1600},[691],"margin-right:2em;",[568,1602],{"className":1603,"style":692},[691],[568,1605,1607,1612],{"className":1606},[627],[568,1608,631,1610],{"className":1609},[627],[568,1611,635],{"style":634},[568,1613,1615],{"className":1614},[639],[568,1616,1618,1642],{"className":1617},[643,644],[568,1619,1621,1639],{"className":1620},[648],[568,1622,1625],{"className":1623,"style":1624},[652],"height:0.207em;",[568,1626,1627,1630],{"style":656},[568,1628],{"className":1629,"style":661},[660],[568,1631,1633],{"className":1632},[665,666,667,668],[568,1634,1636],{"className":1635},[672,668],[568,1637,1450],{"className":1638},[672,668],[568,1640,678],{"className":1641},[677],[568,1643,1645],{"className":1644},[648],[568,1646,1648],{"className":1647,"style":685},[652],[568,1649],{},[568,1651],{"className":1652,"style":692},[691],[568,1654,1657,1666,1670,1706],{"className":1655},[1656],"minner",[568,1658,1662],{"className":1659,"style":1661},[1245,1660],"delimcenter","top:0em;",[568,1663,1173],{"className":1664},[1665,1045],"delimsizing",[568,1667,1669],{"className":1668},[672],"1",[568,1671,1673,1676],{"className":1672},[672],[568,1674,1109],{"className":1675},[672],[568,1677,1679],{"className":1678},[639],[568,1680,1682],{"className":1681},[643],[568,1683,1685],{"className":1684},[648],[568,1686,1689],{"className":1687,"style":1688},[652],"height:0.8641em;",[568,1690,1691,1694],{"style":1508},[568,1692],{"className":1693,"style":661},[660],[568,1695,1697],{"className":1696},[665,666,667,668],[568,1698,1700,1703],{"className":1699},[672,668],[568,1701,1463],{"className":1702},[672,668],[568,1704,1466],{"className":1705},[672,668],[568,1707,1709],{"className":1708,"style":1661},[1278,1660],[568,1710,1182],{"className":1711},[1665,1045],[568,1713],{"className":1714,"style":1071},[691],[568,1716,959],{"className":1717},[1075],[568,1719],{"className":1720,"style":1071},[691],[568,1722,1724,1728,1731],{"className":1723},[618],[568,1725],{"className":1726,"style":1727},[622],"height:0.7278em;vertical-align:-0.0833em;",[568,1729,1463],{"className":1730},[672],[568,1732,1466],{"className":1733},[672],[564,1735,1736,1737,1844,1845],{},"Gleichung lösen: Aus ",[568,1738,1740,1769],{"className":1739},[571],[568,1741,1743],{"className":1742},[575],[577,1744,1745],{"xmlns":579},[581,1746,1747,1766],{},[584,1748,1749,1760,1762,1764],{},[587,1750,1751,1757],{},[584,1752,1753,1755],{},[592,1754,594],{},[596,1756,598],{},[1107,1758,1759],{},"2",[592,1761,604],{},[596,1763,959],{},[1107,1765,1414],{},[606,1767,1768],{"encoding":608},"\\log_2 x = 5",[568,1770,1772,1835],{"className":1771,"ariaHidden":614},[613],[568,1773,1775,1778,1820,1823,1826,1829,1832],{"className":1774},[618],[568,1776],{"className":1777,"style":623},[622],[568,1779,1781,1786],{"className":1780},[627],[568,1782,631,1784],{"className":1783},[627],[568,1785,635],{"style":634},[568,1787,1789],{"className":1788},[639],[568,1790,1792,1812],{"className":1791},[643,644],[568,1793,1795,1809],{"className":1794},[648],[568,1796,1798],{"className":1797,"style":1624},[652],[568,1799,1800,1803],{"style":656},[568,1801],{"className":1802,"style":661},[660],[568,1804,1806],{"className":1805},[665,666,667,668],[568,1807,1759],{"className":1808},[672,668],[568,1810,678],{"className":1811},[677],[568,1813,1815],{"className":1814},[648],[568,1816,1818],{"className":1817,"style":685},[652],[568,1819],{},[568,1821],{"className":1822,"style":692},[691],[568,1824,604],{"className":1825},[672,673],[568,1827],{"className":1828,"style":1071},[691],[568,1830,959],{"className":1831},[1075],[568,1833],{"className":1834,"style":1071},[691],[568,1836,1838,1841],{"className":1837},[618],[568,1839],{"className":1840,"style":1141},[622],[568,1842,1414],{"className":1843},[672]," wird durch Potenzieren mit der Basis ",[568,1846,1848,1861],{"className":1847},[571],[568,1849,1851],{"className":1850},[575],[577,1852,1853],{"xmlns":579},[581,1854,1855,1859],{},[584,1856,1857],{},[1107,1858,1759],{},[606,1860,1759],{"encoding":608},[568,1862,1864],{"className":1863,"ariaHidden":614},[613],[568,1865,1867,1870],{"className":1866},[618],[568,1868],{"className":1869,"style":1141},[622],[568,1871,1759],{"className":1872},[672],[568,1874,1876],{"className":1875},[1396],[568,1877,1879,1926],{"className":1878},[571],[568,1880,1882],{"className":1881},[575],[577,1883,1884],{"xmlns":579,"display":1405},[581,1885,1886,1923],{},[584,1887,1888,1890,1892,1910,1912,1918,1920],{},[592,1889,604],{},[596,1891,959],{},[827,1893,1894,1896],{},[1107,1895,1759],{},[584,1897,1898,1908],{},[587,1899,1900,1906],{},[584,1901,1902,1904],{},[592,1903,594],{},[596,1905,598],{},[1107,1907,1759],{},[592,1909,604],{},[596,1911,959],{},[827,1913,1914,1916],{},[1107,1915,1759],{},[1107,1917,1414],{},[596,1919,959],{},[1107,1921,1922],{},"32",[606,1924,1925],{"encoding":608},"x = 2^{\\log_2 x} = 2^5 = 32",[568,1927,1929,1947,2046,2090],{"className":1928,"ariaHidden":614},[613],[568,1930,1932,1935,1938,1941,1944],{"className":1931},[618],[568,1933],{"className":1934,"style":722},[622],[568,1936,604],{"className":1937},[672,673],[568,1939],{"className":1940,"style":1071},[691],[568,1942,959],{"className":1943},[1075],[568,1945],{"className":1946,"style":1071},[691],[568,1948,1950,1953,2037,2040,2043],{"className":1949},[618],[568,1951],{"className":1952,"style":1487},[622],[568,1954,1956,1959],{"className":1955},[672],[568,1957,1759],{"className":1958},[672],[568,1960,1962],{"className":1961},[639],[568,1963,1965],{"className":1964},[643],[568,1966,1968],{"className":1967},[648],[568,1969,1971],{"className":1970,"style":1487},[652],[568,1972,1973,1976],{"style":1508},[568,1974],{"className":1975,"style":661},[660],[568,1977,1979],{"className":1978},[665,666,667,668],[568,1980,1982,2031,2034],{"className":1981},[672,668],[568,1983,1985,1997],{"className":1984},[627,668],[568,1986,1988,1991,1994],{"className":1987},[627,668],[568,1989,1013],{"className":1990},[668],[568,1992,1017],{"className":1993},[668],[568,1995,635],{"className":1996,"style":634},[668],[568,1998,2000],{"className":1999},[639],[568,2001,2003,2023],{"className":2002},[643,644],[568,2004,2006,2020],{"className":2005},[648],[568,2007,2009],{"className":2008,"style":1545},[652],[568,2010,2011,2014],{"style":1036},[568,2012],{"className":2013,"style":1040},[660],[568,2015,2017],{"className":2016},[665,1044,1045,668],[568,2018,1759],{"className":2019},[672,668],[568,2021,678],{"className":2022},[677],[568,2024,2026],{"className":2025},[648],[568,2027,2029],{"className":2028,"style":1058},[652],[568,2030],{},[568,2032],{"className":2033,"style":1064},[691,668],[568,2035,604],{"className":2036},[672,673,668],[568,2038],{"className":2039,"style":1071},[691],[568,2041,959],{"className":2042},[1075],[568,2044],{"className":2045,"style":1071},[691],[568,2047,2049,2052,2081,2084,2087],{"className":2048},[618],[568,2050],{"className":2051,"style":1688},[622],[568,2053,2055,2058],{"className":2054},[672],[568,2056,1759],{"className":2057},[672],[568,2059,2061],{"className":2060},[639],[568,2062,2064],{"className":2063},[643],[568,2065,2067],{"className":2066},[648],[568,2068,2070],{"className":2069,"style":1688},[652],[568,2071,2072,2075],{"style":1508},[568,2073],{"className":2074,"style":661},[660],[568,2076,2078],{"className":2077},[665,666,667,668],[568,2079,1414],{"className":2080},[672,668],[568,2082],{"className":2083,"style":1071},[691],[568,2085,959],{"className":2086},[1075],[568,2088],{"className":2089,"style":1071},[691],[568,2091,2093,2096],{"className":2092},[618],[568,2094],{"className":2095,"style":1141},[622],[568,2097,1922],{"className":2098},[672],[564,2100,2101],{},"Term vereinfachen mit einem Potenzgesetz:",[568,2103,2105],{"className":2104},[1396],[568,2106,2108,2192],{"className":2107},[571],[568,2109,2111],{"className":2110},[575],[577,2112,2113],{"xmlns":579,"display":1405},[581,2114,2115,2189],{},[584,2116,2117,2141,2143,2161,2164,2170,2172,2175,2177,2179,2181,2183,2185,2187],{},[827,2118,2119,2122],{},[1107,2120,2121],{},"3",[584,2123,2124,2134,2136,2139],{},[587,2125,2126,2132],{},[584,2127,2128,2130],{},[592,2129,594],{},[596,2131,598],{},[1107,2133,2121],{},[592,2135,604],{},[596,2137,2138],{},"+",[1107,2140,1759],{},[596,2142,959],{},[827,2144,2145,2147],{},[1107,2146,2121],{},[584,2148,2149,2159],{},[587,2150,2151,2157],{},[584,2152,2153,2155],{},[592,2154,594],{},[596,2156,598],{},[1107,2158,2121],{},[592,2160,604],{},[596,2162,2163],{},"⋅",[827,2165,2166,2168],{},[1107,2167,2121],{},[1107,2169,1759],{},[596,2171,959],{},[1107,2173,2174],{},"9",[592,2176,604],{},[691,2178],{"width":1439},[596,2180,1173],{"stretchy":1172},[592,2182,604],{},[596,2184,1105],{},[1107,2186,1109],{},[596,2188,1182],{"stretchy":1172},[606,2190,2191],{"encoding":608},"3^{\\log_3 x + 2} = 3^{\\log_3 x} \\cdot 3^2 = 9x \\qquad (x > 0)",[568,2193,2195,2301,2401,2445,2475],{"className":2194,"ariaHidden":614},[613],[568,2196,2198,2201,2292,2295,2298],{"className":2197},[618],[568,2199],{"className":2200,"style":1487},[622],[568,2202,2204,2207],{"className":2203},[672],[568,2205,2121],{"className":2206},[672],[568,2208,2210],{"className":2209},[639],[568,2211,2213],{"className":2212},[643],[568,2214,2216],{"className":2215},[648],[568,2217,2219],{"className":2218,"style":1487},[652],[568,2220,2221,2224],{"style":1508},[568,2222],{"className":2223,"style":661},[660],[568,2225,2227],{"className":2226},[665,666,667,668],[568,2228,2230,2279,2282,2285,2289],{"className":2229},[672,668],[568,2231,2233,2245],{"className":2232},[627,668],[568,2234,2236,2239,2242],{"className":2235},[627,668],[568,2237,1013],{"className":2238},[668],[568,2240,1017],{"className":2241},[668],[568,2243,635],{"className":2244,"style":634},[668],[568,2246,2248],{"className":2247},[639],[568,2249,2251,2271],{"className":2250},[643,644],[568,2252,2254,2268],{"className":2253},[648],[568,2255,2257],{"className":2256,"style":1545},[652],[568,2258,2259,2262],{"style":1036},[568,2260],{"className":2261,"style":1040},[660],[568,2263,2265],{"className":2264},[665,1044,1045,668],[568,2266,2121],{"className":2267},[672,668],[568,2269,678],{"className":2270},[677],[568,2272,2274],{"className":2273},[648],[568,2275,2277],{"className":2276,"style":1058},[652],[568,2278],{},[568,2280],{"className":2281,"style":1064},[691,668],[568,2283,604],{"className":2284},[672,673,668],[568,2286,2138],{"className":2287},[2288,668],"mbin",[568,2290,1759],{"className":2291},[672,668],[568,2293],{"className":2294,"style":1071},[691],[568,2296,959],{"className":2297},[1075],[568,2299],{"className":2300,"style":1071},[691],[568,2302,2304,2307,2391,2395,2398],{"className":2303},[618],[568,2305],{"className":2306,"style":1487},[622],[568,2308,2310,2313],{"className":2309},[672],[568,2311,2121],{"className":2312},[672],[568,2314,2316],{"className":2315},[639],[568,2317,2319],{"className":2318},[643],[568,2320,2322],{"className":2321},[648],[568,2323,2325],{"className":2324,"style":1487},[652],[568,2326,2327,2330],{"style":1508},[568,2328],{"className":2329,"style":661},[660],[568,2331,2333],{"className":2332},[665,666,667,668],[568,2334,2336,2385,2388],{"className":2335},[672,668],[568,2337,2339,2351],{"className":2338},[627,668],[568,2340,2342,2345,2348],{"className":2341},[627,668],[568,2343,1013],{"className":2344},[668],[568,2346,1017],{"className":2347},[668],[568,2349,635],{"className":2350,"style":634},[668],[568,2352,2354],{"className":2353},[639],[568,2355,2357,2377],{"className":2356},[643,644],[568,2358,2360,2374],{"className":2359},[648],[568,2361,2363],{"className":2362,"style":1545},[652],[568,2364,2365,2368],{"style":1036},[568,2366],{"className":2367,"style":1040},[660],[568,2369,2371],{"className":2370},[665,1044,1045,668],[568,2372,2121],{"className":2373},[672,668],[568,2375,678],{"className":2376},[677],[568,2378,2380],{"className":2379},[648],[568,2381,2383],{"className":2382,"style":1058},[652],[568,2384],{},[568,2386],{"className":2387,"style":1064},[691,668],[568,2389,604],{"className":2390},[672,673,668],[568,2392],{"className":2393,"style":2394},[691],"margin-right:0.2222em;",[568,2396,2163],{"className":2397},[2288],[568,2399],{"className":2400,"style":2394},[691],[568,2402,2404,2407,2436,2439,2442],{"className":2403},[618],[568,2405],{"className":2406,"style":1688},[622],[568,2408,2410,2413],{"className":2409},[672],[568,2411,2121],{"className":2412},[672],[568,2414,2416],{"className":2415},[639],[568,2417,2419],{"className":2418},[643],[568,2420,2422],{"className":2421},[648],[568,2423,2425],{"className":2424,"style":1688},[652],[568,2426,2427,2430],{"style":1508},[568,2428],{"className":2429,"style":661},[660],[568,2431,2433],{"className":2432},[665,666,667,668],[568,2434,1759],{"className":2435},[672,668],[568,2437],{"className":2438,"style":1071},[691],[568,2440,959],{"className":2441},[1075],[568,2443],{"className":2444,"style":1071},[691],[568,2446,2448,2451,2454,2457,2460,2463,2466,2469,2472],{"className":2447},[618],[568,2449],{"className":2450,"style":1199},[622],[568,2452,2174],{"className":2453},[672],[568,2455,604],{"className":2456},[672,673],[568,2458],{"className":2459,"style":1600},[691],[568,2461,1173],{"className":2462},[1245],[568,2464,604],{"className":2465},[672,673],[568,2467],{"className":2468,"style":1071},[691],[568,2470,1105],{"className":2471},[1075],[568,2473],{"className":2474,"style":1071},[691],[568,2476,2478,2481,2484],{"className":2477},[618],[568,2479],{"className":2480,"style":1199},[622],[568,2482,1109],{"className":2483},[672],[568,2485,1182],{"className":2486},[1278],[559,2488,2490],{"id":2489},"typische-fehler","Typische Fehler",[922,2492,2493,2727,3018],{},[925,2494,2495,2496,2697,2698,2726],{},"Verschiedene Basen kürzen: ",[568,2497,2499,2541],{"className":2498},[571],[568,2500,2502],{"className":2501},[575],[577,2503,2504],{"xmlns":579},[581,2505,2506,2538],{},[584,2507,2508,2526,2528,2534,2536],{},[827,2509,2510,2512],{},[1107,2511,1759],{},[584,2513,2514,2524],{},[587,2515,2516,2522],{},[584,2517,2518,2520],{},[592,2519,594],{},[596,2521,598],{},[1107,2523,2121],{},[1107,2525,2174],{},[596,2527,959],{},[827,2529,2530,2532],{},[1107,2531,1759],{},[1107,2533,1759],{},[596,2535,959],{},[1107,2537,1466],{},[606,2539,2540],{"encoding":608},"2^{\\log_3 9} = 2^2 = 4",[568,2542,2544,2643,2688],{"className":2543,"ariaHidden":614},[613],[568,2545,2547,2550,2634,2637,2640],{"className":2546},[618],[568,2548],{"className":2549,"style":974},[622],[568,2551,2553,2556],{"className":2552},[672],[568,2554,1759],{"className":2555},[672],[568,2557,2559],{"className":2558},[639],[568,2560,2562],{"className":2561},[643],[568,2563,2565],{"className":2564},[648],[568,2566,2568],{"className":2567,"style":974},[652],[568,2569,2570,2573],{"style":866},[568,2571],{"className":2572,"style":661},[660],[568,2574,2576],{"className":2575},[665,666,667,668],[568,2577,2579,2628,2631],{"className":2578},[672,668],[568,2580,2582,2594],{"className":2581},[627,668],[568,2583,2585,2588,2591],{"className":2584},[627,668],[568,2586,1013],{"className":2587},[668],[568,2589,1017],{"className":2590},[668],[568,2592,635],{"className":2593,"style":634},[668],[568,2595,2597],{"className":2596},[639],[568,2598,2600,2620],{"className":2599},[643,644],[568,2601,2603,2617],{"className":2602},[648],[568,2604,2606],{"className":2605,"style":1545},[652],[568,2607,2608,2611],{"style":1036},[568,2609],{"className":2610,"style":1040},[660],[568,2612,2614],{"className":2613},[665,1044,1045,668],[568,2615,2121],{"className":2616},[672,668],[568,2618,678],{"className":2619},[677],[568,2621,2623],{"className":2622},[648],[568,2624,2626],{"className":2625,"style":1058},[652],[568,2627],{},[568,2629],{"className":2630,"style":1064},[691,668],[568,2632,2174],{"className":2633},[672,668],[568,2635],{"className":2636,"style":1071},[691],[568,2638,959],{"className":2639},[1075],[568,2641],{"className":2642,"style":1071},[691],[568,2644,2646,2650,2679,2682,2685],{"className":2645},[618],[568,2647],{"className":2648,"style":2649},[622],"height:0.8141em;",[568,2651,2653,2656],{"className":2652},[672],[568,2654,1759],{"className":2655},[672],[568,2657,2659],{"className":2658},[639],[568,2660,2662],{"className":2661},[643],[568,2663,2665],{"className":2664},[648],[568,2666,2668],{"className":2667,"style":2649},[652],[568,2669,2670,2673],{"style":866},[568,2671],{"className":2672,"style":661},[660],[568,2674,2676],{"className":2675},[665,666,667,668],[568,2677,1759],{"className":2678},[672,668],[568,2680],{"className":2681,"style":1071},[691],[568,2683,959],{"className":2684},[1075],[568,2686],{"className":2687,"style":1071},[691],[568,2689,2691,2694],{"className":2690},[618],[568,2692],{"className":2693,"style":1141},[622],[568,2695,1466],{"className":2696},[672],", nicht ",[568,2699,2701,2714],{"className":2700},[571],[568,2702,2704],{"className":2703},[575],[577,2705,2706],{"xmlns":579},[581,2707,2708,2712],{},[584,2709,2710],{},[1107,2711,2174],{},[606,2713,2174],{"encoding":608},[568,2715,2717],{"className":2716,"ariaHidden":614},[613],[568,2718,2720,2723],{"className":2719},[618],[568,2721],{"className":2722,"style":1141},[622],[568,2724,2174],{"className":2725},[672],". Die Umkehrung funktioniert nur bei gleicher Basis.",[925,2728,2729,2730,2780,2781,2920,2921,3017],{},"Die Bedingung ",[568,2731,2733,2750],{"className":2732},[571],[568,2734,2736],{"className":2735},[575],[577,2737,2738],{"xmlns":579},[581,2739,2740,2748],{},[584,2741,2742,2744,2746],{},[592,2743,604],{},[596,2745,1105],{},[1107,2747,1109],{},[606,2749,1112],{"encoding":608},[568,2751,2753,2771],{"className":2752,"ariaHidden":614},[613],[568,2754,2756,2759,2762,2765,2768],{"className":2755},[618],[568,2757],{"className":2758,"style":1122},[622],[568,2760,604],{"className":2761},[672,673],[568,2763],{"className":2764,"style":1071},[691],[568,2766,1105],{"className":2767},[1075],[568,2769],{"className":2770,"style":1071},[691],[568,2772,2774,2777],{"className":2773},[618],[568,2775],{"className":2776,"style":1141},[622],[568,2778,1109],{"className":2779},[672]," vergessen: ",[568,2782,2784,2820],{"className":2783},[571],[568,2785,2787],{"className":2786},[575],[577,2788,2789],{"xmlns":579},[581,2790,2791,2817],{},[584,2792,2793],{},[827,2794,2795,2797],{},[1107,2796,1759],{},[584,2798,2799,2809,2811,2813,2815],{},[587,2800,2801,2807],{},[584,2802,2803,2805],{},[592,2804,594],{},[596,2806,598],{},[1107,2808,1759],{},[596,2810,1173],{"stretchy":1172},[596,2812,1463],{},[1107,2814,1466],{},[596,2816,1182],{"stretchy":1172},[606,2818,2819],{"encoding":608},"2^{\\log_2(-4)}",[568,2821,2823],{"className":2822,"ariaHidden":614},[613],[568,2824,2826,2830],{"className":2825},[618],[568,2827],{"className":2828,"style":2829},[622],"height:0.888em;",[568,2831,2833,2836],{"className":2832},[672],[568,2834,1759],{"className":2835},[672],[568,2837,2839],{"className":2838},[639],[568,2840,2842],{"className":2841},[643],[568,2843,2845],{"className":2844},[648],[568,2846,2848],{"className":2847,"style":2829},[652],[568,2849,2850,2853],{"style":866},[568,2851],{"className":2852,"style":661},[660],[568,2854,2856],{"className":2855},[665,666,667,668],[568,2857,2859,2908,2911,2914,2917],{"className":2858},[672,668],[568,2860,2862,2874],{"className":2861},[627,668],[568,2863,2865,2868,2871],{"className":2864},[627,668],[568,2866,1013],{"className":2867},[668],[568,2869,1017],{"className":2870},[668],[568,2872,635],{"className":2873,"style":634},[668],[568,2875,2877],{"className":2876},[639],[568,2878,2880,2900],{"className":2879},[643,644],[568,2881,2883,2897],{"className":2882},[648],[568,2884,2886],{"className":2885,"style":1545},[652],[568,2887,2888,2891],{"style":1036},[568,2889],{"className":2890,"style":1040},[660],[568,2892,2894],{"className":2893},[665,1044,1045,668],[568,2895,1759],{"className":2896},[672,668],[568,2898,678],{"className":2899},[677],[568,2901,2903],{"className":2902},[648],[568,2904,2906],{"className":2905,"style":1058},[652],[568,2907],{},[568,2909,1173],{"className":2910},[1245,668],[568,2912,1463],{"className":2913},[672,668],[568,2915,1466],{"className":2916},[672,668],[568,2918,1182],{"className":2919},[1278,668]," ist nicht definiert, weil ",[568,2922,2924,2954],{"className":2923},[571],[568,2925,2927],{"className":2926},[575],[577,2928,2929],{"xmlns":579},[581,2930,2931,2951],{},[584,2932,2933,2943,2945,2947,2949],{},[587,2934,2935,2941],{},[584,2936,2937,2939],{},[592,2938,594],{},[596,2940,598],{},[1107,2942,1759],{},[596,2944,1173],{"stretchy":1172},[596,2946,1463],{},[1107,2948,1466],{},[596,2950,1182],{"stretchy":1172},[606,2952,2953],{"encoding":608},"\\log_2(-4)",[568,2955,2957],{"className":2956,"ariaHidden":614},[613],[568,2958,2960,2963,3005,3008,3011,3014],{"className":2959},[618],[568,2961],{"className":2962,"style":1199},[622],[568,2964,2966,2971],{"className":2965},[627],[568,2967,631,2969],{"className":2968},[627],[568,2970,635],{"style":634},[568,2972,2974],{"className":2973},[639],[568,2975,2977,2997],{"className":2976},[643,644],[568,2978,2980,2994],{"className":2979},[648],[568,2981,2983],{"className":2982,"style":1624},[652],[568,2984,2985,2988],{"style":656},[568,2986],{"className":2987,"style":661},[660],[568,2989,2991],{"className":2990},[665,666,667,668],[568,2992,1759],{"className":2993},[672,668],[568,2995,678],{"className":2996},[677],[568,2998,3000],{"className":2999},[648],[568,3001,3003],{"className":3002,"style":685},[652],[568,3004],{},[568,3006,1173],{"className":3007},[1245],[568,3009,1463],{"className":3010},[672],[568,3012,1466],{"className":3013},[672],[568,3015,1182],{"className":3016},[1278]," nicht existiert.",[925,3019,3020,3021,3142,3143,2697,3171,3223],{},"Den Logarithmus wie einen Faktor behandeln: ",[568,3022,3024,3056],{"className":3023},[571],[568,3025,3027],{"className":3026},[575],[577,3028,3029],{"xmlns":579},[581,3030,3031,3053],{},[584,3032,3033,3043,3045,3051],{},[587,3034,3035,3041],{},[584,3036,3037,3039],{},[592,3038,594],{},[596,3040,598],{},[592,3042,601],{},[596,3044,1173],{"stretchy":1172},[827,3046,3047,3049],{},[592,3048,601],{},[592,3050,604],{},[596,3052,1182],{"stretchy":1172},[606,3054,3055],{"encoding":608},"\\log_a(a^x)",[568,3057,3059],{"className":3058,"ariaHidden":614},[613],[568,3060,3062,3065,3107,3110,3139],{"className":3061},[618],[568,3063],{"className":3064,"style":1199},[622],[568,3066,3068,3073],{"className":3067},[627],[568,3069,631,3071],{"className":3070},[627],[568,3072,635],{"style":634},[568,3074,3076],{"className":3075},[639],[568,3077,3079,3099],{"className":3078},[643,644],[568,3080,3082,3096],{"className":3081},[648],[568,3083,3085],{"className":3084,"style":653},[652],[568,3086,3087,3090],{"style":656},[568,3088],{"className":3089,"style":661},[660],[568,3091,3093],{"className":3092},[665,666,667,668],[568,3094,601],{"className":3095},[672,673,668],[568,3097,678],{"className":3098},[677],[568,3100,3102],{"className":3101},[648],[568,3103,3105],{"className":3104,"style":685},[652],[568,3106],{},[568,3108,1173],{"className":3109},[1245],[568,3111,3113,3116],{"className":3112},[672],[568,3114,601],{"className":3115},[672,673],[568,3117,3119],{"className":3118},[639],[568,3120,3122],{"className":3121},[643],[568,3123,3125],{"className":3124},[648],[568,3126,3128],{"className":3127,"style":845},[652],[568,3129,3130,3133],{"style":866},[568,3131],{"className":3132,"style":661},[660],[568,3134,3136],{"className":3135},[665,666,667,668],[568,3137,604],{"className":3138},[672,673,668],[568,3140,1182],{"className":3141},[1278]," ist ",[568,3144,3146,3159],{"className":3145},[571],[568,3147,3149],{"className":3148},[575],[577,3150,3151],{"xmlns":579},[581,3152,3153,3157],{},[584,3154,3155],{},[592,3156,604],{},[606,3158,604],{"encoding":608},[568,3160,3162],{"className":3161,"ariaHidden":614},[613],[568,3163,3165,3168],{"className":3164},[618],[568,3166],{"className":3167,"style":722},[622],[568,3169,604],{"className":3170},[672,673],[568,3172,3174,3192],{"className":3173},[571],[568,3175,3177],{"className":3176},[575],[577,3178,3179],{"xmlns":579},[581,3180,3181,3189],{},[584,3182,3183,3185,3187],{},[592,3184,601],{},[596,3186,2163],{},[592,3188,604],{},[606,3190,3191],{"encoding":608},"a \\cdot x",[568,3193,3195,3214],{"className":3194,"ariaHidden":614},[613],[568,3196,3198,3202,3205,3208,3211],{"className":3197},[618],[568,3199],{"className":3200,"style":3201},[622],"height:0.4445em;",[568,3203,601],{"className":3204},[672,673],[568,3206],{"className":3207,"style":2394},[691],[568,3209,2163],{"className":3210},[2288],[568,3212],{"className":3213,"style":2394},[691],[568,3215,3217,3220],{"className":3216},[618],[568,3218],{"className":3219,"style":722},[622],[568,3221,604],{"className":3222},[672,673],".",{"title":3225,"searchDepth":3226,"depth":3226,"links":3227},"",2,[3228,3229,3230],{"id":561,"depth":3226,"text":562},{"id":1391,"depth":3226,"text":1392},{"id":2489,"depth":3226,"text":2490},[3232,3234,3236,3238,3241,3243,3245,3248],{"lhs":3233,"rhs":604},"a^log(x, a)",{"lhs":3235,"rhs":604},"log(a^x, a)",{"lhs":3237,"rhs":1429},"5^log(7, 5)",{"lhs":3239,"rhs":3240},"log10(10^(-4))","-4",{"lhs":3242,"rhs":1414},"log(32, 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style=\"height:0.8389em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">1\u003C\u002Fspan>\u003Cspan class=\"mpunct\">;\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">links\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>x\u003C\u002Fmi>\u003Cmo>>\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">x > 0,\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.5782em;vertical-align:-0.0391em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8389em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">rechts\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>x\u003C\u002Fmi>\u003Cmo>∈\u003C\u002Fmo>\u003Cmi mathvariant=\"double-struck\">R\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">x \\in \\mathbb{R}\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.5782em;vertical-align:-0.0391em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">∈\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6889em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathbb\">R\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","log-inverse","a^{\\log_a x} = x, \\qquad \\log_a\\left(a^x\\right) = x","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" 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