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a^x",[572,1132,1134,1152],{"className":1133,"ariaHidden":636},[635],[572,1135,1137,1140,1143,1146,1149],{"className":1136},[640],[572,1138],{"className":1139,"style":921},[644],[572,1141,908],{"className":1142},[649,653],[572,1144],{"className":1145,"style":739},[691],[572,1147,613],{"className":1148},[743],[572,1150],{"className":1151,"style":739},[691],[572,1153,1155,1158],{"className":1154},[640],[572,1156],{"className":1157,"style":645},[644],[572,1159,1161,1164],{"className":1160},[649],[572,1162,596],{"className":1163},[649,653],[572,1165,1167],{"className":1166},[657],[572,1168,1170],{"className":1169},[661],[572,1171,1173],{"className":1172},[665],[572,1174,1176],{"className":1175,"style":645},[669],[572,1177,1178,1181],{"style":672},[572,1179],{"className":1180,"style":677},[676],[572,1182,1184],{"className":1183},[681,682,683,684],[572,1185,599],{"className":1186},[649,653,684],[572,1188,1190,1212],{"className":1189},[575],[572,1191,1193],{"className":1192},[579],[581,1194,1195],{"xmlns":583},[585,1196,1197,1209],{},[588,1198,1199,1201,1203],{},[594,1200,1025],{},[601,1202,613],{},[591,1204,1205,1207],{},[594,1206,596],{},[594,1208,610],{},[628,1210,1211],{"encoding":630},"v = a^y",[572,1213,1215,1233],{"className":1214,"ariaHidden":636},[635],[572,1216,1218,1221,1224,1227,1230],{"className":1217},[640],[572,1219],{"className":1220,"style":921},[644],[572,1222,1025],{"className":1223,"style":735},[649,653],[572,1225],{"className":1226,"style":739},[691],[572,1228,613],{"className":1229},[743],[572,1231],{"className":1232,"style":739},[691],[572,1234,1236,1239],{"className":1235},[640],[572,1237],{"className":1238,"style":645},[644],[572,1240,1242,1245],{"className":1241},[649],[572,1243,596],{"className":1244},[649,653],[572,1246,1248],{"className":1247},[657],[572,1249,1251],{"className":1250},[661],[572,1252,1254],{"className":1253},[665],[572,1255,1257],{"className":1256,"style":645},[669],[572,1258,1259,1262],{"style":672},[572,1260],{"className":1261,"style":677},[676],[572,1263,1265],{"className":1264},[681,682,683,684],[572,1266,610],{"className":1267,"style":735},[649,653,684],". Dann gilt",[572,1270,1273],{"className":1271},[1272],"katex-display",[572,1274,1276,1364],{"className":1275},[575],[572,1277,1279],{"className":1278},[579],[581,1280,1282],{"xmlns":583,"display":1281},"block",[585,1283,1284,1361],{},[588,1285,1286,1288,1290,1292,1294,1300,1302,1308,1310,1322,1325,1328,1330,1340,1344,1346,1348,1350,1353,1355,1357,1359],{},[594,1287,908],{},[601,1289,603],{},[594,1291,1025],{},[601,1293,613],{},[591,1295,1296,1298],{},[594,1297,596],{},[594,1299,599],{},[601,1301,603],{},[591,1303,1304,1306],{},[594,1305,596],{},[594,1307,610],{},[601,1309,613],{},[591,1311,1312,1314],{},[594,1313,596],{},[588,1315,1316,1318,1320],{},[594,1317,599],{},[601,1319,624],{},[594,1321,610],{},[691,1323],{"width":1324},"1em",[601,1326,1327],{},"⇒",[691,1329],{"width":1324},[895,1331,1332,1338],{},[588,1333,1334,1336],{},[594,1335,901],{},[601,1337,810],{},[594,1339,596],{},[601,1341,1343],{"stretchy":1342},"false","(",[594,1345,908],{},[601,1347,603],{},[594,1349,1025],{},[601,1351,1352],{"stretchy":1342},")",[601,1354,613],{},[594,1356,599],{},[601,1358,624],{},[594,1360,610],{},[628,1362,1363],{"encoding":630},"u \\cdot v = a^x \\cdot a^y = a^{x+y}\n\\quad\\Rightarrow\\quad\n\\log_a (u \\cdot v) = x + y",[572,1365,1367,1386,1404,1450,1494,1555,1620,1642,1661],{"className":1366,"ariaHidden":636},[635],[572,1368,1370,1374,1377,1380,1383],{"className":1369},[640],[572,1371],{"className":1372,"style":1373},[644],"height:0.4445em;",[572,1375,908],{"className":1376},[649,653],[572,1378],{"className":1379,"style":692},[691],[572,1381,603],{"className":1382},[696],[572,1384],{"className":1385,"style":692},[691],[572,1387,1389,1392,1395,1398,1401],{"className":1388},[640],[572,1390],{"className":1391,"style":921},[644],[572,1393,1025],{"className":1394,"style":735},[649,653],[572,1396],{"className":1397,"style":739},[691],[572,1399,613],{"className":1400},[743],[572,1402],{"className":1403,"style":739},[691],[572,1405,1407,1411,1441,1444,1447],{"className":1406},[640],[572,1408],{"className":1409,"style":1410},[644],"height:0.7144em;",[572,1412,1414,1417],{"className":1413},[649],[572,1415,596],{"className":1416},[649,653],[572,1418,1420],{"className":1419},[657],[572,1421,1423],{"className":1422},[661],[572,1424,1426],{"className":1425},[665],[572,1427,1429],{"className":1428,"style":1410},[669],[572,1430,1432,1435],{"style":1431},"top:-3.113em;margin-right:0.05em;",[572,1433],{"className":1434,"style":677},[676],[572,1436,1438],{"className":1437},[681,682,683,684],[572,1439,599],{"className":1440},[649,653,684],[572,1442],{"className":1443,"style":692},[691],[572,1445,603],{"className":1446},[696],[572,1448],{"className":1449,"style":692},[691],[572,1451,1453,1456,1485,1488,1491],{"className":1452},[640],[572,1454],{"className":1455,"style":1410},[644],[572,1457,1459,1462],{"className":1458},[649],[572,1460,596],{"className":1461},[649,653],[572,1463,1465],{"className":1464},[657],[572,1466,1468],{"className":1467},[661],[572,1469,1471],{"className":1470},[665],[572,1472,1474],{"className":1473,"style":1410},[669],[572,1475,1476,1479],{"style":1431},[572,1477],{"className":1478,"style":677},[676],[572,1480,1482],{"className":1481},[681,682,683,684],[572,1483,610],{"className":1484,"style":735},[649,653,684],[572,1486],{"className":1487,"style":739},[691],[572,1489,613],{"className":1490},[743],[572,1492],{"className":1493,"style":739},[691],[572,1495,1497,1501,1539,1543,1546,1549,1552],{"className":1496},[640],[572,1498],{"className":1499,"style":1500},[644],"height:0.8213em;",[572,1502,1504,1507],{"className":1503},[649],[572,1505,596],{"className":1506},[649,653],[572,1508,1510],{"className":1509},[657],[572,1511,1513],{"className":1512},[661],[572,1514,1516],{"className":1515},[665],[572,1517,1519],{"className":1518,"style":1500},[669],[572,1520,1521,1524],{"style":1431},[572,1522],{"className":1523,"style":677},[676],[572,1525,1527],{"className":1526},[681,682,683,684],[572,1528,1530,1533,1536],{"className":1529},[649,684],[572,1531,599],{"className":1532},[649,653,684],[572,1534,624],{"className":1535},[696,684],[572,1537,610],{"className":1538,"style":735},[649,653,684],[572,1540],{"className":1541,"style":1542},[691],"margin-right:1em;",[572,1544],{"className":1545,"style":739},[691],[572,1547,1327],{"className":1548},[743],[572,1550],{"className":1551,"style":1542},[691],[572,1553],{"className":1554,"style":739},[691],[572,1556,1558,1562,1604,1608,1611,1614,1617],{"className":1557},[640],[572,1559],{"className":1560,"style":1561},[644],"height:1em;vertical-align:-0.25em;",[572,1563,1565,1570],{"className":1564},[827],[572,1566,947,1568],{"className":1567},[827],[572,1569,832],{"style":831},[572,1571,1573],{"className":1572},[657],[572,1574,1576,1596],{"className":1575},[661,956],[572,1577,1579,1593],{"className":1578},[665],[572,1580,1582],{"className":1581,"style":963},[669],[572,1583,1584,1587],{"style":966},[572,1585],{"className":1586,"style":677},[676],[572,1588,1590],{"className":1589},[681,682,683,684],[572,1591,596],{"className":1592},[649,653,684],[572,1594,980],{"className":1595},[979],[572,1597,1599],{"className":1598},[665],[572,1600,1602],{"className":1601,"style":987},[669],[572,1603],{},[572,1605,1343],{"className":1606},[1607],"mopen",[572,1609,908],{"className":1610},[649,653],[572,1612],{"className":1613,"style":692},[691],[572,1615,603],{"className":1616},[696],[572,1618],{"className":1619,"style":692},[691],[572,1621,1623,1626,1629,1633,1636,1639],{"className":1622},[640],[572,1624],{"className":1625,"style":1561},[644],[572,1627,1025],{"className":1628,"style":735},[649,653],[572,1630,1352],{"className":1631},[1632],"mclose",[572,1634],{"className":1635,"style":739},[691],[572,1637,613],{"className":1638},[743],[572,1640],{"className":1641,"style":739},[691],[572,1643,1645,1649,1652,1655,1658],{"className":1644},[640],[572,1646],{"className":1647,"style":1648},[644],"height:0.6667em;vertical-align:-0.0833em;",[572,1650,599],{"className":1651},[649,653],[572,1653],{"className":1654,"style":692},[691],[572,1656,624],{"className":1657},[696],[572,1659],{"className":1660,"style":692},[691],[572,1662,1664,1667],{"className":1663},[640],[572,1665],{"className":1666,"style":1038},[644],[572,1668,610],{"className":1669,"style":735},[649,653],[558,1671,1673],{"id":1672},"beispiele","Beispiele",[572,1675,1677],{"className":1676},[1272],[572,1678,1680,1758],{"className":1679},[575],[572,1681,1683],{"className":1682},[579],[581,1684,1685],{"xmlns":583,"display":1281},[585,1686,1687,1755],{},[588,1688,1689,1701,1703,1706,1708,1711,1713,1715,1725,1727,1729,1739,1741,1743,1746,1748,1750,1752],{},[895,1690,1691,1697],{},[588,1692,1693,1695],{},[594,1694,901],{},[601,1696,810],{},[1698,1699,1700],"mn",{},"2",[601,1702,1343],{"stretchy":1342},[1698,1704,1705],{},"8",[601,1707,603],{},[1698,1709,1710],{},"4",[601,1712,1352],{"stretchy":1342},[601,1714,613],{},[895,1716,1717,1723],{},[588,1718,1719,1721],{},[594,1720,901],{},[601,1722,810],{},[1698,1724,1700],{},[1698,1726,1705],{},[601,1728,624],{},[895,1730,1731,1737],{},[588,1732,1733,1735],{},[594,1734,901],{},[601,1736,810],{},[1698,1738,1700],{},[1698,1740,1710],{},[601,1742,613],{},[1698,1744,1745],{},"3",[601,1747,624],{},[1698,1749,1700],{},[601,1751,613],{},[1698,1753,1754],{},"5",[628,1756,1757],{"encoding":630},"\\log_2 (8 \\cdot 4) = \\log_2 8 + \\log_2 4 = 3 + 2 = 5",[572,1759,1761,1825,1846,1909,1972,1991,2010],{"className":1760,"ariaHidden":636},[635],[572,1762,1764,1767,1810,1813,1816,1819,1822],{"className":1763},[640],[572,1765],{"className":1766,"style":1561},[644],[572,1768,1770,1775],{"className":1769},[827],[572,1771,947,1773],{"className":1772},[827],[572,1774,832],{"style":831},[572,1776,1778],{"className":1777},[657],[572,1779,1781,1802],{"className":1780},[661,956],[572,1782,1784,1799],{"className":1783},[665],[572,1785,1788],{"className":1786,"style":1787},[669],"height:0.207em;",[572,1789,1790,1793],{"style":966},[572,1791],{"className":1792,"style":677},[676],[572,1794,1796],{"className":1795},[681,682,683,684],[572,1797,1700],{"className":1798},[649,684],[572,1800,980],{"className":1801},[979],[572,1803,1805],{"className":1804},[665],[572,1806,1808],{"className":1807,"style":987},[669],[572,1809],{},[572,1811,1343],{"className":1812},[1607],[572,1814,1705],{"className":1815},[649],[572,1817],{"className":1818,"style":692},[691],[572,1820,603],{"className":1821},[696],[572,1823],{"className":1824,"style":692},[691],[572,1826,1828,1831,1834,1837,1840,1843],{"className":1827},[640],[572,1829],{"className":1830,"style":1561},[644],[572,1832,1710],{"className":1833},[649],[572,1835,1352],{"className":1836},[1632],[572,1838],{"className":1839,"style":739},[691],[572,1841,613],{"className":1842},[743],[572,1844],{"className":1845,"style":739},[691],[572,1847,1849,1852,1894,1897,1900,1903,1906],{"className":1848},[640],[572,1850],{"className":1851,"style":940},[644],[572,1853,1855,1860],{"className":1854},[827],[572,1856,947,1858],{"className":1857},[827],[572,1859,832],{"style":831},[572,1861,1863],{"className":1862},[657],[572,1864,1866,1886],{"className":1865},[661,956],[572,1867,1869,1883],{"className":1868},[665],[572,1870,1872],{"className":1871,"style":1787},[669],[572,1873,1874,1877],{"style":966},[572,1875],{"className":1876,"style":677},[676],[572,1878,1880],{"className":1879},[681,682,683,684],[572,1881,1700],{"className":1882},[649,684],[572,1884,980],{"className":1885},[979],[572,1887,1889],{"className":1888},[665],[572,1890,1892],{"className":1891,"style":987},[669],[572,1893],{},[572,1895],{"className":1896,"style":993},[691],[572,1898,1705],{"className":1899},[649],[572,1901],{"className":1902,"style":692},[691],[572,1904,624],{"className":1905},[696],[572,1907],{"className":1908,"style":692},[691],[572,1910,1912,1915,1957,1960,1963,1966,1969],{"className":1911},[640],[572,1913],{"className":1914,"style":940},[644],[572,1916,1918,1923],{"className":1917},[827],[572,1919,947,1921],{"className":1920},[827],[572,1922,832],{"style":831},[572,1924,1926],{"className":1925},[657],[572,1927,1929,1949],{"className":1928},[661,956],[572,1930,1932,1946],{"className":1931},[665],[572,1933,1935],{"className":1934,"style":1787},[669],[572,1936,1937,1940],{"style":966},[572,1938],{"className":1939,"style":677},[676],[572,1941,1943],{"className":1942},[681,682,683,684],[572,1944,1700],{"className":1945},[649,684],[572,1947,980],{"className":1948},[979],[572,1950,1952],{"className":1951},[665],[572,1953,1955],{"className":1954,"style":987},[669],[572,1956],{},[572,1958],{"className":1959,"style":993},[691],[572,1961,1710],{"className":1962},[649],[572,1964],{"className":1965,"style":739},[691],[572,1967,613],{"className":1968},[743],[572,1970],{"className":1971,"style":739},[691],[572,1973,1975,1979,1982,1985,1988],{"className":1974},[640],[572,1976],{"className":1977,"style":1978},[644],"height:0.7278em;vertical-align:-0.0833em;",[572,1980,1745],{"className":1981},[649],[572,1983],{"className":1984,"style":692},[691],[572,1986,624],{"className":1987},[696],[572,1989],{"className":1990,"style":692},[691],[572,1992,1994,1998,2001,2004,2007],{"className":1993},[640],[572,1995],{"className":1996,"style":1997},[644],"height:0.6444em;",[572,1999,1700],{"className":2000},[649],[572,2002],{"className":2003,"style":739},[691],[572,2005,613],{"className":2006},[743],[572,2008],{"className":2009,"style":739},[691],[572,2011,2013,2016],{"className":2012},[640],[572,2014],{"className":2015,"style":1997},[644],[572,2017,1754],{"className":2018},[649],[572,2020,2022],{"className":2021},[1272],[572,2023,2025,2076],{"className":2024},[575],[572,2026,2028],{"className":2027},[579],[581,2029,2030],{"xmlns":583,"display":1281},[585,2031,2032,2073],{},[588,2033,2034,2036,2038,2041,2043,2045,2047,2049,2051,2053,2055,2058,2061,2064,2066,2068,2070],{},[594,2035,807],{},[601,2037,810],{},[1698,2039,2040],{},"200",[601,2042,613],{},[594,2044,807],{},[601,2046,810],{},[1698,2048,1700],{},[601,2050,624],{},[594,2052,807],{},[601,2054,810],{},[1698,2056,2057],{},"100",[601,2059,2060],{},"≈",[1698,2062,2063],{},"0,301",[601,2065,624],{},[1698,2067,1700],{},[601,2069,613],{},[1698,2071,2072],{},"2,301",[628,2074,2075],{"encoding":630},"\\lg 200 = \\lg 2 + \\lg 100 \\approx 0{,}301 + 2 = 2{,}301",[572,2077,2079,2105,2131,2157,2189,2207],{"className":2078,"ariaHidden":636},[635],[572,2080,2082,2085,2090,2093,2096,2099,2102],{"className":2081},[640],[572,2083],{"className":2084,"style":823},[644],[572,2086,828,2088],{"className":2087},[827],[572,2089,832],{"style":831},[572,2091],{"className":2092,"style":993},[691],[572,2094,2040],{"className":2095},[649],[572,2097],{"className":2098,"style":739},[691],[572,2100,613],{"className":2101},[743],[572,2103],{"className":2104,"style":739},[691],[572,2106,2108,2111,2116,2119,2122,2125,2128],{"className":2107},[640],[572,2109],{"className":2110,"style":823},[644],[572,2112,828,2114],{"className":2113},[827],[572,2115,832],{"style":831},[572,2117],{"className":2118,"style":993},[691],[572,2120,1700],{"className":2121},[649],[572,2123],{"className":2124,"style":692},[691],[572,2126,624],{"className":2127},[696],[572,2129],{"className":2130,"style":692},[691],[572,2132,2134,2137,2142,2145,2148,2151,2154],{"className":2133},[640],[572,2135],{"className":2136,"style":823},[644],[572,2138,828,2140],{"className":2139},[827],[572,2141,832],{"style":831},[572,2143],{"className":2144,"style":993},[691],[572,2146,2057],{"className":2147},[649],[572,2149],{"className":2150,"style":739},[691],[572,2152,2060],{"className":2153},[743],[572,2155],{"className":2156,"style":739},[691],[572,2158,2160,2164,2168,2176,2180,2183,2186],{"className":2159},[640],[572,2161],{"className":2162,"style":2163},[644],"height:0.8389em;vertical-align:-0.1944em;",[572,2165,2167],{"className":2166},[649],"0",[572,2169,2171],{"className":2170},[649],[572,2172,2175],{"className":2173},[2174],"mpunct",",",[572,2177,2179],{"className":2178},[649],"301",[572,2181],{"className":2182,"style":692},[691],[572,2184,624],{"className":2185},[696],[572,2187],{"className":2188,"style":692},[691],[572,2190,2192,2195,2198,2201,2204],{"className":2191},[640],[572,2193],{"className":2194,"style":1997},[644],[572,2196,1700],{"className":2197},[649],[572,2199],{"className":2200,"style":739},[691],[572,2202,613],{"className":2203},[743],[572,2205],{"className":2206,"style":739},[691],[572,2208,2210,2213,2216,2222],{"className":2209},[640],[572,2211],{"className":2212,"style":2163},[644],[572,2214,1700],{"className":2215},[649],[572,2217,2219],{"className":2218},[649],[572,2220,2175],{"className":2221},[2174],[572,2223,2179],{"className":2224},[649],[558,2226,2228],{"id":2227},"typische-fehler","Typische Fehler",[2230,2231,2232,2546],"ul",{},[2233,2234,2235,2236,2545],"li",{},"Die Regel auf Summen anwenden: ",[572,2237,2239,2301],{"className":2238},[575],[572,2240,2242],{"className":2241},[579],[581,2243,2244],{"xmlns":583},[585,2245,2246,2298],{},[588,2247,2248,2258,2260,2262,2264,2266,2268,2272,2282,2284,2286,2296],{},[895,2249,2250,2256],{},[588,2251,2252,2254],{},[594,2253,901],{},[601,2255,810],{},[594,2257,596],{},[601,2259,1343],{"stretchy":1342},[594,2261,908],{},[601,2263,624],{},[594,2265,1025],{},[601,2267,1352],{"stretchy":1342},[601,2269,2271],{"mathvariant":2270},"normal","≠",[895,2273,2274,2280],{},[588,2275,2276,2278],{},[594,2277,901],{},[601,2279,810],{},[594,2281,596],{},[594,2283,908],{},[601,2285,624],{},[895,2287,2288,2294],{},[588,2289,2290,2292],{},[594,2291,901],{},[601,2293,810],{},[594,2295,596],{},[594,2297,1025],{},[628,2299,2300],{"encoding":630},"\\log_a (u + v) \\neq \\log_a u + \\log_a v",[572,2302,2304,2367,2428,2491],{"className":2303,"ariaHidden":636},[635],[572,2305,2307,2310,2352,2355,2358,2361,2364],{"className":2306},[640],[572,2308],{"className":2309,"style":1561},[644],[572,2311,2313,2318],{"className":2312},[827],[572,2314,947,2316],{"className":2315},[827],[572,2317,832],{"style":831},[572,2319,2321],{"className":2320},[657],[572,2322,2324,2344],{"className":2323},[661,956],[572,2325,2327,2341],{"className":2326},[665],[572,2328,2330],{"className":2329,"style":963},[669],[572,2331,2332,2335],{"style":966},[572,2333],{"className":2334,"style":677},[676],[572,2336,2338],{"className":2337},[681,682,683,684],[572,2339,596],{"className":2340},[649,653,684],[572,2342,980],{"className":2343},[979],[572,2345,2347],{"className":2346},[665],[572,2348,2350],{"className":2349,"style":987},[669],[572,2351],{},[572,2353,1343],{"className":2354},[1607],[572,2356,908],{"className":2357},[649,653],[572,2359],{"className":2360,"style":692},[691],[572,2362,624],{"className":2363},[696],[572,2365],{"className":2366,"style":692},[691],[572,2368,2370,2373,2376,2379,2382,2425],{"className":2369},[640],[572,2371],{"className":2372,"style":1561},[644],[572,2374,1025],{"className":2375,"style":735},[649,653],[572,2377,1352],{"className":2378},[1632],[572,2380],{"className":2381,"style":739},[691],[572,2383,2385,2418,2422],{"className":2384},[743],[572,2386,2388],{"className":2387},[743],[572,2389,2392],{"className":2390},[649,2391],"vbox",[572,2393,2396],{"className":2394},[2395],"thinbox",[572,2397,2400,2403,2414],{"className":2398},[2399],"rlap",[572,2401],{"className":2402,"style":823},[644],[572,2404,2407],{"className":2405},[2406],"inner",[572,2408,2410],{"className":2409},[649],[572,2411,2413],{"className":2412},[743],"",[572,2415],{"className":2416},[2417],"fix",[572,2419],{"className":2420},[691,2421],"nobreak",[572,2423,613],{"className":2424},[743],[572,2426],{"className":2427,"style":739},[691],[572,2429,2431,2434,2476,2479,2482,2485,2488],{"className":2430},[640],[572,2432],{"className":2433,"style":940},[644],[572,2435,2437,2442],{"className":2436},[827],[572,2438,947,2440],{"className":2439},[827],[572,2441,832],{"style":831},[572,2443,2445],{"className":2444},[657],[572,2446,2448,2468],{"className":2447},[661,956],[572,2449,2451,2465],{"className":2450},[665],[572,2452,2454],{"className":2453,"style":963},[669],[572,2455,2456,2459],{"style":966},[572,2457],{"className":2458,"style":677},[676],[572,2460,2462],{"className":2461},[681,682,683,684],[572,2463,596],{"className":2464},[649,653,684],[572,2466,980],{"className":2467},[979],[572,2469,2471],{"className":2470},[665],[572,2472,2474],{"className":2473,"style":987},[669],[572,2475],{},[572,2477],{"className":2478,"style":993},[691],[572,2480,908],{"className":2481},[649,653],[572,2483],{"className":2484,"style":692},[691],[572,2486,624],{"className":2487},[696],[572,2489],{"className":2490,"style":692},[691],[572,2492,2494,2497,2539,2542],{"className":2493},[640],[572,2495],{"className":2496,"style":940},[644],[572,2498,2500,2505],{"className":2499},[827],[572,2501,947,2503],{"className":2502},[827],[572,2504,832],{"style":831},[572,2506,2508],{"className":2507},[657],[572,2509,2511,2531],{"className":2510},[661,956],[572,2512,2514,2528],{"className":2513},[665],[572,2515,2517],{"className":2516,"style":963},[669],[572,2518,2519,2522],{"style":966},[572,2520],{"className":2521,"style":677},[676],[572,2523,2525],{"className":2524},[681,682,683,684],[572,2526,596],{"className":2527},[649,653,684],[572,2529,980],{"className":2530},[979],[572,2532,2534],{"className":2533},[665],[572,2535,2537],{"className":2536,"style":987},[669],[572,2538],{},[572,2540],{"className":2541,"style":993},[691],[572,2543,1025],{"className":2544,"style":735},[649,653],". Für den Logarithmus einer Summe gibt es keine Vereinfachung.",[2233,2547,2548,2549,2710,2711,867],{},"Logarithmen multiplizieren: ",[572,2550,2552,2590],{"className":2551},[575],[572,2553,2555],{"className":2554},[579],[581,2556,2557],{"xmlns":583},[585,2558,2559,2587],{},[588,2560,2561,2571,2573,2575,2585],{},[895,2562,2563,2569],{},[588,2564,2565,2567],{},[594,2566,901],{},[601,2568,810],{},[594,2570,596],{},[594,2572,908],{},[601,2574,603],{},[895,2576,2577,2583],{},[588,2578,2579,2581],{},[594,2580,901],{},[601,2582,810],{},[594,2584,596],{},[594,2586,1025],{},[628,2588,2589],{"encoding":630},"\\log_a u \\cdot \\log_a v",[572,2591,2593,2656],{"className":2592,"ariaHidden":636},[635],[572,2594,2596,2599,2641,2644,2647,2650,2653],{"className":2595},[640],[572,2597],{"className":2598,"style":940},[644],[572,2600,2602,2607],{"className":2601},[827],[572,2603,947,2605],{"className":2604},[827],[572,2606,832],{"style":831},[572,2608,2610],{"className":2609},[657],[572,2611,2613,2633],{"className":2612},[661,956],[572,2614,2616,2630],{"className":2615},[665],[572,2617,2619],{"className":2618,"style":963},[669],[572,2620,2621,2624],{"style":966},[572,2622],{"className":2623,"style":677},[676],[572,2625,2627],{"className":2626},[681,682,683,684],[572,2628,596],{"className":2629},[649,653,684],[572,2631,980],{"className":2632},[979],[572,2634,2636],{"className":2635},[665],[572,2637,2639],{"className":2638,"style":987},[669],[572,2640],{},[572,2642],{"className":2643,"style":993},[691],[572,2645,908],{"className":2646},[649,653],[572,2648],{"className":2649,"style":692},[691],[572,2651,603],{"className":2652},[696],[572,2654],{"className":2655,"style":692},[691],[572,2657,2659,2662,2704,2707],{"className":2658},[640],[572,2660],{"className":2661,"style":940},[644],[572,2663,2665,2670],{"className":2664},[827],[572,2666,947,2668],{"className":2667},[827],[572,2669,832],{"style":831},[572,2671,2673],{"className":2672},[657],[572,2674,2676,2696],{"className":2675},[661,956],[572,2677,2679,2693],{"className":2678},[665],[572,2680,2682],{"className":2681,"style":963},[669],[572,2683,2684,2687],{"style":966},[572,2685],{"className":2686,"style":677},[676],[572,2688,2690],{"className":2689},[681,682,683,684],[572,2691,596],{"className":2692},[649,653,684],[572,2694,980],{"className":2695},[979],[572,2697,2699],{"className":2698},[665],[572,2700,2702],{"className":2701,"style":987},[669],[572,2703],{},[572,2705],{"className":2706,"style":993},[691],[572,2708,1025],{"className":2709,"style":735},[649,653]," ist etwas anderes als ",[572,2712,2714,2746],{"className":2713},[575],[572,2715,2717],{"className":2716},[579],[581,2718,2719],{"xmlns":583},[585,2720,2721,2743],{},[588,2722,2723,2733,2735,2737,2739,2741],{},[895,2724,2725,2731],{},[588,2726,2727,2729],{},[594,2728,901],{},[601,2730,810],{},[594,2732,596],{},[601,2734,1343],{"stretchy":1342},[594,2736,908],{},[601,2738,603],{},[594,2740,1025],{},[601,2742,1352],{"stretchy":1342},[628,2744,2745],{"encoding":630},"\\log_a (u \\cdot v)",[572,2747,2749,2812],{"className":2748,"ariaHidden":636},[635],[572,2750,2752,2755,2797,2800,2803,2806,2809],{"className":2751},[640],[572,2753],{"className":2754,"style":1561},[644],[572,2756,2758,2763],{"className":2757},[827],[572,2759,947,2761],{"className":2760},[827],[572,2762,832],{"style":831},[572,2764,2766],{"className":2765},[657],[572,2767,2769,2789],{"className":2768},[661,956],[572,2770,2772,2786],{"className":2771},[665],[572,2773,2775],{"className":2774,"style":963},[669],[572,2776,2777,2780],{"style":966},[572,2778],{"className":2779,"style":677},[676],[572,2781,2783],{"className":2782},[681,682,683,684],[572,2784,596],{"className":2785},[649,653,684],[572,2787,980],{"className":2788},[979],[572,2790,2792],{"className":2791},[665],[572,2793,2795],{"className":2794,"style":987},[669],[572,2796],{},[572,2798,1343],{"className":2799},[1607],[572,2801,908],{"className":2802},[649,653],[572,2804],{"className":2805,"style":692},[691],[572,2807,603],{"className":2808},[696],[572,2810],{"className":2811,"style":692},[691],[572,2813,2815,2818,2821],{"className":2814},[640],[572,2816],{"className":2817,"style":1561},[644],[572,2819,1025],{"className":2820,"style":735},[649,653],[572,2822,1352],{"className":2823},[1632],{"title":2825,"searchDepth":2826,"depth":2826,"links":2827},"",2,[2828,2829,2830,2831],{"id":560,"depth":2826,"text":561},{"id":873,"depth":2826,"text":874},{"id":1672,"depth":2826,"text":1673},{"id":2227,"depth":2826,"text":2228},[2833,2836,2839,2841],{"lhs":2834,"rhs":2835},"log(u*v, a)","log(u, a) + log(v, a)",{"lhs":2837,"rhs":2838},"log(8*4, 2)","log(8, 2) + log(4, 2)",{"lhs":2840,"rhs":1754},"log(32, 2)",{"lhs":2842,"rhs":2843},"log10(200)","log10(2) + 2","a > 0,\\ a \\neq 1,\\ u, v > 0","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>a\u003C\u002Fmi>\u003Cmo>>\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">a > 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\">a\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\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>a\u003C\u002Fmi>\u003Cmo mathvariant=\"normal\">≠\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">a \\neq 1,\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:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">\u003Cspan class=\"mrel\">\u003Cspan class=\"mord katex-vbox\">\u003Cspan class=\"katex-thinbox\">\u003Cspan class=\"rlap\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-inner\">\u003Cspan class=\"mord\">\u003Cspan class=\"mrel\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-fix\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace nobreak\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\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\">1\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>u\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>v\u003C\u002Fmi>\u003Cmo>>\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">u, v > 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:0.7335em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">u\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" 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