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Die y-Achse ist eine Asymptote.",[846,967,968,969,1038,1039,1100,1101,838],{},"Der Graph geht immer durch ",[572,970,972,999],{"className":971},[575],[572,973,975],{"className":974},[579],[581,976,977],{"xmlns":583},[585,978,979,996],{},[588,980,981,985,988,991,993],{},[697,982,984],{"stretchy":983},"false","(",[867,986,987],{},"1",[697,989,990],{},"∣",[867,992,869],{},[697,994,995],{"stretchy":983},")",[595,997,998],{"encoding":597},"(1 \\mid 0)",[572,1000,1002,1025],{"className":1001,"ariaHidden":602},[601],[572,1003,1005,1009,1013,1016,1019,1022],{"className":1004},[606],[572,1006],{"className":1007,"style":1008},[610],"height:1em;vertical-align:-0.25em;",[572,1010,984],{"className":1011},[1012],"mopen",[572,1014,987],{"className":1015},[615],[572,1017],{"className":1018,"style":727},[726],[572,1020,990],{"className":1021},[731],[572,1023],{"className":1024,"style":727},[726],[572,1026,1028,1031,1034],{"className":1027},[606],[572,1029],{"className":1030,"style":1008},[610],[572,1032,869],{"className":1033},[615],[572,1035,995],{"className":1036},[1037],"mclose"," und ",[572,1040,1042,1064],{"className":1041},[575],[572,1043,1045],{"className":1044},[579],[581,1046,1047],{"xmlns":583},[585,1048,1049,1061],{},[588,1050,1051,1053,1055,1057,1059],{},[697,1052,984],{"stretchy":983},[591,1054,593],{},[697,1056,990],{},[867,1058,987],{},[697,1060,995],{"stretchy":983},[595,1062,1063],{"encoding":597},"(b \\mid 1)",[572,1065,1067,1088],{"className":1066,"ariaHidden":602},[601],[572,1068,1070,1073,1076,1079,1082,1085],{"className":1069},[606],[572,1071],{"className":1072,"style":1008},[610],[572,1074,984],{"className":1075},[1012],[572,1077,593],{"className":1078},[615,616],[572,1080],{"className":1081,"style":727},[726],[572,1083,990],{"className":1084},[731],[572,1086],{"className":1087,"style":727},[726],[572,1089,1091,1094,1097],{"className":1090},[606],[572,1092],{"className":1093,"style":1008},[610],[572,1095,987],{"className":1096},[615],[572,1098,995],{"className":1099},[1037],". Die einzige Nullstelle ist ",[572,1102,1104,1122],{"className":1103},[575],[572,1105,1107],{"className":1106},[579],[581,1108,1109],{"xmlns":583},[585,1110,1111,1119],{},[588,1112,1113,1115,1117],{},[591,1114,661],{},[697,1116,800],{},[867,1118,987],{},[595,1120,1121],{"encoding":597},"x = 1",[572,1123,1125,1143],{"className":1124,"ariaHidden":602},[601],[572,1126,1128,1131,1134,1137,1140],{"className":1127},[606],[572,1129],{"className":1130,"style":673},[610],[572,1132,661],{"className":1133},[615,616],[572,1135],{"className":1136,"style":727},[726],[572,1138,800],{"className":1139},[731],[572,1141],{"className":1142,"style":727},[726],[572,1144,1146,1149],{"className":1145},[606],[572,1147],{"className":1148,"style":901},[610],[572,1150,987],{"className":1151},[615],[846,1153,1154,1155,1207,1208,1283],{},"Für ",[572,1156,1158,1176],{"className":1157},[575],[572,1159,1161],{"className":1160},[579],[581,1162,1163],{"xmlns":583},[585,1164,1165,1173],{},[588,1166,1167,1169,1171],{},[591,1168,593],{},[697,1170,865],{},[867,1172,987],{},[595,1174,1175],{"encoding":597},"b > 1",[572,1177,1179,1198],{"className":1178,"ariaHidden":602},[601],[572,1180,1182,1186,1189,1192,1195],{"className":1181},[606],[572,1183],{"className":1184,"style":1185},[610],"height:0.7335em;vertical-align:-0.0391em;",[572,1187,593],{"className":1188},[615,616],[572,1190],{"className":1191,"style":727},[726],[572,1193,865],{"className":1194},[731],[572,1196],{"className":1197,"style":727},[726],[572,1199,1201,1204],{"className":1200},[606],[572,1202],{"className":1203,"style":901},[610],[572,1205,987],{"className":1206},[615]," steigt der Graph, aber immer langsamer; für ",[572,1209,1211,1234],{"className":1210},[575],[572,1212,1214],{"className":1213},[579],[581,1215,1216],{"xmlns":583},[585,1217,1218,1231],{},[588,1219,1220,1222,1225,1227,1229],{},[867,1221,869],{},[697,1223,1224],{},"\u003C",[591,1226,593],{},[697,1228,1224],{},[867,1230,987],{},[595,1232,1233],{"encoding":597},"0 \u003C b \u003C 1",[572,1235,1237,1256,1274],{"className":1236,"ariaHidden":602},[601],[572,1238,1240,1244,1247,1250,1253],{"className":1239},[606],[572,1241],{"className":1242,"style":1243},[610],"height:0.6835em;vertical-align:-0.0391em;",[572,1245,869],{"className":1246},[615],[572,1248],{"className":1249,"style":727},[726],[572,1251,1224],{"className":1252},[731],[572,1254],{"className":1255,"style":727},[726],[572,1257,1259,1262,1265,1268,1271],{"className":1258},[606],[572,1260],{"className":1261,"style":1185},[610],[572,1263,593],{"className":1264},[615,616],[572,1266],{"className":1267,"style":727},[726],[572,1269,1224],{"className":1270},[731],[572,1272],{"className":1273,"style":727},[726],[572,1275,1277,1280],{"className":1276},[606],[572,1278],{"className":1279,"style":901},[610],[572,1281,987],{"className":1282},[615]," fällt er.",[564,1285,1286,1287,1290,1291,1424,1425,1290,1428,1554,1555,838],{},"Wichtige Sonderfälle sind der ",[568,1288,1289],{},"natürliche Logarithmus"," ",[572,1292,1294,1331],{"className":1293},[575],[572,1295,1297],{"className":1296},[579],[581,1298,1299],{"xmlns":583},[585,1300,1301,1328],{},[588,1302,1303,1306,1309,1311,1313,1326],{},[591,1304,1305],{},"ln",[697,1307,1308],{},"⁡",[591,1310,661],{},[697,1312,800],{},[1314,1315,1316,1323],"msub",{},[588,1317,1318,1321],{},[591,1319,1320],{},"log",[697,1322,1308],{},[591,1324,1325],{},"e",[591,1327,661],{},[595,1329,1330],{"encoding":597},"\\ln x = \\log_e x",[572,1332,1334,1360],{"className":1333,"ariaHidden":602},[601],[572,1335,1337,1340,1344,1348,1351,1354,1357],{"className":1336},[606],[572,1338],{"className":1339,"style":611},[610],[572,1341,1305],{"className":1342},[1343],"mop",[572,1345],{"className":1346,"style":1347},[726],"margin-right:0.1667em;",[572,1349,661],{"className":1350},[615,616],[572,1352],{"className":1353,"style":727},[726],[572,1355,800],{"className":1356},[731],[572,1358],{"className":1359,"style":727},[726],[572,1361,1363,1367,1418,1421],{"className":1362},[606],[572,1364],{"className":1365,"style":1366},[610],"height:0.9386em;vertical-align:-0.2441em;",[572,1368,1370,1378],{"className":1369},[1343],[572,1371,1373,1374],{"className":1372},[1343],"lo",[572,1375,1377],{"style":1376},"margin-right:0.0139em;","g",[572,1379,1381],{"className":1380},[750],[572,1382,1385,1409],{"className":1383},[754,1384],"vlist-t2",[572,1386,1388,1404],{"className":1387},[758],[572,1389,1392],{"className":1390,"style":1391},[762],"height:0.0573em;",[572,1393,1395,1398],{"style":1394},"top:-2.4559em;margin-right:0.05em;",[572,1396],{"className":1397,"style":771},[770],[572,1399,1401],{"className":1400},[775,776,777,778],[572,1402,1325],{"className":1403},[615,616,778],[572,1405,1408],{"className":1406},[1407],"vlist-s","​",[572,1410,1412],{"className":1411},[758],[572,1413,1416],{"className":1414,"style":1415},[762],"height:0.2441em;",[572,1417],{},[572,1419],{"className":1420,"style":1347},[726],[572,1422,661],{"className":1423},[615,616]," und der ",[568,1426,1427],{},"Zehnerlogarithmus",[572,1429,1431,1465],{"className":1430},[575],[572,1432,1434],{"className":1433},[579],[581,1435,1436],{"xmlns":583},[585,1437,1438,1462],{},[588,1439,1440,1443,1445,1447,1449,1460],{},[591,1441,1442],{},"lg",[697,1444,1308],{},[591,1446,661],{},[697,1448,800],{},[1314,1450,1451,1457],{},[588,1452,1453,1455],{},[591,1454,1320],{},[697,1456,1308],{},[867,1458,1459],{},"10",[591,1461,661],{},[595,1463,1464],{"encoding":597},"\\lg x = \\log_{10} x",[572,1466,1468,1496],{"className":1467,"ariaHidden":602},[601],[572,1469,1471,1475,1481,1484,1487,1490,1493],{"className":1470},[606],[572,1472],{"className":1473,"style":1474},[610],"height:0.8889em;vertical-align:-0.1944em;",[572,1476,1478,1479],{"className":1477},[1343],"l",[572,1480,1377],{"style":1376},[572,1482],{"className":1483,"style":1347},[726],[572,1485,661],{"className":1486},[615,616],[572,1488],{"className":1489,"style":727},[726],[572,1491,800],{"className":1492},[731],[572,1494],{"className":1495,"style":727},[726],[572,1497,1499,1502,1548,1551],{"className":1498},[606],[572,1500],{"className":1501,"style":1366},[610],[572,1503,1505,1510],{"className":1504},[1343],[572,1506,1373,1508],{"className":1507},[1343],[572,1509,1377],{"style":1376},[572,1511,1513],{"className":1512},[750],[572,1514,1516,1540],{"className":1515},[754,1384],[572,1517,1519,1537],{"className":1518},[758],[572,1520,1523],{"className":1521,"style":1522},[762],"height:0.207em;",[572,1524,1525,1528],{"style":1394},[572,1526],{"className":1527,"style":771},[770],[572,1529,1531],{"className":1530},[775,776,777,778],[572,1532,1534],{"className":1533},[615,778],[572,1535,1459],{"className":1536},[615,778],[572,1538,1408],{"className":1539},[1407],[572,1541,1543],{"className":1542},[758],[572,1544,1546],{"className":1545,"style":1415},[762],[572,1547],{},[572,1549],{"className":1550,"style":1347},[726],[572,1552,661],{"className":1553},[615,616],". Jede andere Basis lässt sich darauf zurückführen: ",[572,1556,1558,1603],{"className":1557},[575],[572,1559,1561],{"className":1560},[579],[581,1562,1563],{"xmlns":583},[585,1564,1565,1600],{},[588,1566,1567,1577,1579,1581],{},[1314,1568,1569,1575],{},[588,1570,1571,1573],{},[591,1572,1320],{},[697,1574,1308],{},[591,1576,593],{},[591,1578,661],{},[697,1580,800],{},[1582,1583,1584,1592],"mfrac",{},[588,1585,1586,1588,1590],{},[591,1587,1305],{},[697,1589,1308],{},[591,1591,661],{},[588,1593,1594,1596,1598],{},[591,1595,1305],{},[697,1597,1308],{},[591,1599,593],{},[595,1601,1602],{"encoding":597},"\\log_b x = \\frac{\\ln x}{\\ln b}",[572,1604,1606,1670],{"className":1605,"ariaHidden":602},[601],[572,1607,1609,1612,1655,1658,1661,1664,1667],{"className":1608},[606],[572,1610],{"className":1611,"style":1366},[610],[572,1613,1615,1620],{"className":1614},[1343],[572,1616,1373,1618],{"className":1617},[1343],[572,1619,1377],{"style":1376},[572,1621,1623],{"className":1622},[750],[572,1624,1626,1647],{"className":1625},[754,1384],[572,1627,1629,1644],{"className":1628},[758],[572,1630,1633],{"className":1631,"style":1632},[762],"height:0.242em;",[572,1634,1635,1638],{"style":1394},[572,1636],{"className":1637,"style":771},[770],[572,1639,1641],{"className":1640},[775,776,777,778],[572,1642,593],{"className":1643},[615,616,778],[572,1645,1408],{"className":1646},[1407],[572,1648,1650],{"className":1649},[758],[572,1651,1653],{"className":1652,"style":1415},[762],[572,1654],{},[572,1656],{"className":1657,"style":1347},[726],[572,1659,661],{"className":1660},[615,616],[572,1662],{"className":1663,"style":727},[726],[572,1665,800],{"className":1666},[731],[572,1668],{"className":1669,"style":727},[726],[572,1671,1673,1677],{"className":1672},[606],[572,1674],{"className":1675,"style":1676},[610],"height:1.2251em;vertical-align:-0.345em;",[572,1678,1680,1684,1777],{"className":1679},[615],[572,1681],{"className":1682},[1012,1683],"nulldelimiter",[572,1685,1687],{"className":1686},[1582],[572,1688,1690,1768],{"className":1689},[754,1384],[572,1691,1693,1765],{"className":1692},[758],[572,1694,1697,1727,1738],{"className":1695,"style":1696},[762],"height:0.8801em;",[572,1698,1700,1704],{"style":1699},"top:-2.655em;",[572,1701],{"className":1702,"style":1703},[770],"height:3em;",[572,1705,1707],{"className":1706},[775,776,777,778],[572,1708,1710,1720,1724],{"className":1709},[615,778],[572,1711,1713,1716],{"className":1712},[1343,778],[572,1714,1478],{"className":1715},[778],[572,1717,1719],{"className":1718},[778],"n",[572,1721],{"className":1722,"style":1723},[726,778],"margin-right:0.1952em;",[572,1725,593],{"className":1726},[615,616,778],[572,1728,1730,1733],{"style":1729},"top:-3.23em;",[572,1731],{"className":1732,"style":1703},[770],[572,1734],{"className":1735,"style":1737},[1736],"frac-line","border-bottom-width:0.04em;",[572,1739,1741,1744],{"style":1740},"top:-3.394em;",[572,1742],{"className":1743,"style":1703},[770],[572,1745,1747],{"className":1746},[775,776,777,778],[572,1748,1750,1759,1762],{"className":1749},[615,778],[572,1751,1753,1756],{"className":1752},[1343,778],[572,1754,1478],{"className":1755},[778],[572,1757,1719],{"className":1758},[778],[572,1760],{"className":1761,"style":1723},[726,778],[572,1763,661],{"className":1764},[615,616,778],[572,1766,1408],{"className":1767},[1407],[572,1769,1771],{"className":1770},[758],[572,1772,1775],{"className":1773,"style":1774},[762],"height:0.345em;",[572,1776],{},[572,1778],{"className":1779},[1037,1683],[559,1781,1783],{"id":1782},"beispiele","Beispiele",[572,1785,1788],{"className":1786},[1787],"katex-display",[572,1789,1791,1881],{"className":1790},[575],[572,1792,1794],{"className":1793},[579],[581,1795,1797],{"xmlns":583,"display":1796},"block",[585,1798,1799,1878],{},[588,1800,1801,1812,1815,1817,1820,1823,1826,1836,1839,1841,1844,1846,1848,1850,1852,1854,1857,1859,1861,1863,1865,1867,1869,1872,1875],{},[1314,1802,1803,1809],{},[588,1804,1805,1807],{},[591,1806,1320],{},[697,1808,1308],{},[867,1810,1811],{},"2",[867,1813,1814],{},"8",[697,1816,800],{},[867,1818,1819],{},"3",[697,1821,1822],{"separator":602},",",[726,1824],{"width":1825},"2em",[1314,1827,1828,1834],{},[588,1829,1830,1832],{},[591,1831,1320],{},[697,1833,1308],{},[867,1835,1811],{},[867,1837,1838],{},"0,5",[697,1840,800],{},[697,1842,1843],{},"−",[867,1845,987],{},[697,1847,1822],{"separator":602},[726,1849],{"width":1825},[591,1851,1442],{},[697,1853,1308],{},[867,1855,1856],{},"1000",[697,1858,800],{},[867,1860,1819],{},[697,1862,1822],{"separator":602},[726,1864],{"width":1825},[591,1866,1305],{},[697,1868,1308],{},[867,1870,1871],{},"5",[697,1873,1874],{},"≈",[867,1876,1877],{},"1,61",[595,1879,1880],{"encoding":597},"\\log_2 8 = 3, \\qquad \\log_2 0{,}5 = -1, \\qquad \\lg 1000 = 3, \\qquad \\ln 5 \\approx 1{,}61",[572,1882,1884,1947,2033,2074,2110],{"className":1883,"ariaHidden":602},[601],[572,1885,1887,1890,1932,1935,1938,1941,1944],{"className":1886},[606],[572,1888],{"className":1889,"style":1366},[610],[572,1891,1893,1898],{"className":1892},[1343],[572,1894,1373,1896],{"className":1895},[1343],[572,1897,1377],{"style":1376},[572,1899,1901],{"className":1900},[750],[572,1902,1904,1924],{"className":1903},[754,1384],[572,1905,1907,1921],{"className":1906},[758],[572,1908,1910],{"className":1909,"style":1522},[762],[572,1911,1912,1915],{"style":1394},[572,1913],{"className":1914,"style":771},[770],[572,1916,1918],{"className":1917},[775,776,777,778],[572,1919,1811],{"className":1920},[615,778],[572,1922,1408],{"className":1923},[1407],[572,1925,1927],{"className":1926},[758],[572,1928,1930],{"className":1929,"style":1415},[762],[572,1931],{},[572,1933],{"className":1934,"style":1347},[726],[572,1936,1814],{"className":1937},[615],[572,1939],{"className":1940,"style":727},[726],[572,1942,800],{"className":1943},[731],[572,1945],{"className":1946,"style":727},[726],[572,1948,1950,1953,1956,1960,1964,1967,2009,2012,2015,2021,2024,2027,2030],{"className":1949},[606],[572,1951],{"className":1952,"style":1366},[610],[572,1954,1819],{"className":1955},[615],[572,1957,1822],{"className":1958},[1959],"mpunct",[572,1961],{"className":1962,"style":1963},[726],"margin-right:2em;",[572,1965],{"className":1966,"style":1347},[726],[572,1968,1970,1975],{"className":1969},[1343],[572,1971,1373,1973],{"className":1972},[1343],[572,1974,1377],{"style":1376},[572,1976,1978],{"className":1977},[750],[572,1979,1981,2001],{"className":1980},[754,1384],[572,1982,1984,1998],{"className":1983},[758],[572,1985,1987],{"className":1986,"style":1522},[762],[572,1988,1989,1992],{"style":1394},[572,1990],{"className":1991,"style":771},[770],[572,1993,1995],{"className":1994},[775,776,777,778],[572,1996,1811],{"className":1997},[615,778],[572,1999,1408],{"className":2000},[1407],[572,2002,2004],{"className":2003},[758],[572,2005,2007],{"className":2006,"style":1415},[762],[572,2008],{},[572,2010],{"className":2011,"style":1347},[726],[572,2013,869],{"className":2014},[615],[572,2016,2018],{"className":2017},[615],[572,2019,1822],{"className":2020},[1959],[572,2022,1871],{"className":2023},[615],[572,2025],{"className":2026,"style":727},[726],[572,2028,800],{"className":2029},[731],[572,2031],{"className":2032,"style":727},[726],[572,2034,2036,2039,2042,2045,2048,2051,2054,2059,2062,2065,2068,2071],{"className":2035},[606],[572,2037],{"className":2038,"style":1474},[610],[572,2040,1843],{"className":2041},[615],[572,2043,987],{"className":2044},[615],[572,2046,1822],{"className":2047},[1959],[572,2049],{"className":2050,"style":1963},[726],[572,2052],{"className":2053,"style":1347},[726],[572,2055,1478,2057],{"className":2056},[1343],[572,2058,1377],{"style":1376},[572,2060],{"className":2061,"style":1347},[726],[572,2063,1856],{"className":2064},[615],[572,2066],{"className":2067,"style":727},[726],[572,2069,800],{"className":2070},[731],[572,2072],{"className":2073,"style":727},[726],[572,2075,2077,2080,2083,2086,2089,2092,2095,2098,2101,2104,2107],{"className":2076},[606],[572,2078],{"className":2079,"style":1474},[610],[572,2081,1819],{"className":2082},[615],[572,2084,1822],{"className":2085},[1959],[572,2087],{"className":2088,"style":1963},[726],[572,2090],{"className":2091,"style":1347},[726],[572,2093,1305],{"className":2094},[1343],[572,2096],{"className":2097,"style":1347},[726],[572,2099,1871],{"className":2100},[615],[572,2102],{"className":2103,"style":727},[726],[572,2105,1874],{"className":2106},[731],[572,2108],{"className":2109,"style":727},[726],[572,2111,2113,2117,2120,2126],{"className":2112},[606],[572,2114],{"className":2115,"style":2116},[610],"height:0.8389em;vertical-align:-0.1944em;",[572,2118,987],{"className":2119},[615],[572,2121,2123],{"className":2122},[615],[572,2124,1822],{"className":2125},[1959],[572,2127,2129],{"className":2128},[615],"61",[564,2131,2132,2133,2193,2194,2321,2322,838],{},"Bei der Basis ",[572,2134,2136,2154],{"className":2135},[575],[572,2137,2139],{"className":2138},[579],[581,2140,2141],{"xmlns":583},[585,2142,2143,2151],{},[588,2144,2145,2147,2149],{},[591,2146,593],{},[697,2148,800],{},[867,2150,1838],{},[595,2152,2153],{"encoding":597},"b = 0{,}5",[572,2155,2157,2175],{"className":2156,"ariaHidden":602},[601],[572,2158,2160,2163,2166,2169,2172],{"className":2159},[606],[572,2161],{"className":2162,"style":611},[610],[572,2164,593],{"className":2165},[615,616],[572,2167],{"className":2168,"style":727},[726],[572,2170,800],{"className":2171},[731],[572,2173],{"className":2174,"style":727},[726],[572,2176,2178,2181,2184,2190],{"className":2177},[606],[572,2179],{"className":2180,"style":2116},[610],[572,2182,869],{"className":2183},[615],[572,2185,2187],{"className":2186},[615],[572,2188,1822],{"className":2189},[1959],[572,2191,1871],{"className":2192},[615]," fällt der Graph: ",[572,2195,2197,2228],{"className":2196},[575],[572,2198,2200],{"className":2199},[579],[581,2201,2202],{"xmlns":583},[585,2203,2204,2225],{},[588,2205,2206,2216,2219,2221,2223],{},[1314,2207,2208,2214],{},[588,2209,2210,2212],{},[591,2211,1320],{},[697,2213,1308],{},[867,2215,1838],{},[867,2217,2218],{},"4",[697,2220,800],{},[697,2222,1843],{},[867,2224,1811],{},[595,2226,2227],{"encoding":597},"\\log_{0{,}5} 4 = -2",[572,2229,2231,2308],{"className":2230,"ariaHidden":602},[601],[572,2232,2234,2238,2293,2296,2299,2302,2305],{"className":2233},[606],[572,2235],{"className":2236,"style":2237},[610],"height:1.0747em;vertical-align:-0.3802em;",[572,2239,2241,2246],{"className":2240},[1343],[572,2242,1373,2244],{"className":2243},[1343],[572,2245,1377],{"style":1376},[572,2247,2249],{"className":2248},[750],[572,2250,2252,2284],{"className":2251},[754,1384],[572,2253,2255,2281],{"className":2254},[758],[572,2256,2258],{"className":2257,"style":1522},[762],[572,2259,2260,2263],{"style":1394},[572,2261],{"className":2262,"style":771},[770],[572,2264,2266],{"className":2265},[775,776,777,778],[572,2267,2269,2272,2278],{"className":2268},[615,778],[572,2270,869],{"className":2271},[615,778],[572,2273,2275],{"className":2274},[615,778],[572,2276,1822],{"className":2277},[1959,778],[572,2279,1871],{"className":2280},[615,778],[572,2282,1408],{"className":2283},[1407],[572,2285,2287],{"className":2286},[758],[572,2288,2291],{"className":2289,"style":2290},[762],"height:0.3802em;",[572,2292],{},[572,2294],{"className":2295,"style":1347},[726],[572,2297,2218],{"className":2298},[615],[572,2300],{"className":2301,"style":727},[726],[572,2303,800],{"className":2304},[731],[572,2306],{"className":2307,"style":727},[726],[572,2309,2311,2315,2318],{"className":2310},[606],[572,2312],{"className":2313,"style":2314},[610],"height:0.7278em;vertical-align:-0.0833em;",[572,2316,1843],{"className":2317},[615],[572,2319,1811],{"className":2320},[615],", denn ",[572,2323,2325,2351],{"className":2324},[575],[572,2326,2328],{"className":2327},[579],[581,2329,2330],{"xmlns":583},[585,2331,2332,2348],{},[588,2333,2334,2344,2346],{},[701,2335,2336,2338],{},[867,2337,1838],{},[588,2339,2340,2342],{},[697,2341,1843],{},[867,2343,1811],{},[697,2345,800],{},[867,2347,2218],{},[595,2349,2350],{"encoding":597},"0{,}5^{-2} = 4",[572,2352,2354,2415],{"className":2353,"ariaHidden":602},[601],[572,2355,2357,2361,2364,2370,2406,2409,2412],{"className":2356},[606],[572,2358],{"className":2359,"style":2360},[610],"height:1.0085em;vertical-align:-0.1944em;",[572,2362,869],{"className":2363},[615],[572,2365,2367],{"className":2366},[615],[572,2368,1822],{"className":2369},[1959],[572,2371,2373,2376],{"className":2372},[615],[572,2374,1871],{"className":2375},[615],[572,2377,2379],{"className":2378},[750],[572,2380,2382],{"className":2381},[754],[572,2383,2385],{"className":2384},[758],[572,2386,2389],{"className":2387,"style":2388},[762],"height:0.8141em;",[572,2390,2391,2394],{"style":766},[572,2392],{"className":2393,"style":771},[770],[572,2395,2397],{"className":2396},[775,776,777,778],[572,2398,2400,2403],{"className":2399},[615,778],[572,2401,1843],{"className":2402},[615,778],[572,2404,1811],{"className":2405},[615,778],[572,2407],{"className":2408,"style":727},[726],[572,2410,800],{"className":2411},[731],[572,2413],{"className":2414,"style":727},[726],[572,2416,2418,2421],{"className":2417},[606],[572,2419],{"className":2420,"style":901},[610],[572,2422,2218],{"className":2423},[615],[564,2425,2426,2427,2536,2537,2611,2612,838],{},"Bei ",[572,2428,2430,2467],{"className":2429},[575],[572,2431,2433],{"className":2432},[579],[581,2434,2435],{"xmlns":583},[585,2436,2437,2464],{},[588,2438,2439,2442,2444,2446,2448,2450,2452,2454,2456,2458,2460,2462],{},[591,2440,2441],{},"f",[697,2443,984],{"stretchy":983},[591,2445,661],{},[697,2447,995],{"stretchy":983},[697,2449,800],{},[591,2451,1305],{},[697,2453,1308],{},[697,2455,984],{"stretchy":983},[591,2457,661],{},[697,2459,1843],{},[867,2461,1811],{},[697,2463,995],{"stretchy":983},[595,2465,2466],{"encoding":597},"f(x) = \\ln(x - 2)",[572,2468,2470,2498,2524],{"className":2469,"ariaHidden":602},[601],[572,2471,2473,2476,2480,2483,2486,2489,2492,2495],{"className":2472},[606],[572,2474],{"className":2475,"style":1008},[610],[572,2477,2441],{"className":2478,"style":2479},[615,616],"margin-right:0.1076em;",[572,2481,984],{"className":2482},[1012],[572,2484,661],{"className":2485},[615,616],[572,2487,995],{"className":2488},[1037],[572,2490],{"className":2491,"style":727},[726],[572,2493,800],{"className":2494},[731],[572,2496],{"className":2497,"style":727},[726],[572,2499,2501,2504,2507,2510,2513,2517,2521],{"className":2500},[606],[572,2502],{"className":2503,"style":1008},[610],[572,2505,1305],{"className":2506},[1343],[572,2508,984],{"className":2509},[1012],[572,2511,661],{"className":2512},[615,616],[572,2514],{"className":2515,"style":2516},[726],"margin-right:0.2222em;",[572,2518,1843],{"className":2519},[2520],"mbin",[572,2522],{"className":2523,"style":2516},[726],[572,2525,2527,2530,2533],{"className":2526},[606],[572,2528],{"className":2529,"style":1008},[610],[572,2531,1811],{"className":2532},[615],[572,2534,995],{"className":2535},[1037]," muss das Argument positiv sein: ",[572,2538,2540,2562],{"className":2539},[575],[572,2541,2543],{"className":2542},[579],[581,2544,2545],{"xmlns":583},[585,2546,2547,2559],{},[588,2548,2549,2551,2553,2555,2557],{},[591,2550,661],{},[697,2552,1843],{},[867,2554,1811],{},[697,2556,865],{},[867,2558,869],{},[595,2560,2561],{"encoding":597},"x - 2 > 0",[572,2563,2565,2584,2602],{"className":2564,"ariaHidden":602},[601],[572,2566,2568,2572,2575,2578,2581],{"className":2567},[606],[572,2569],{"className":2570,"style":2571},[610],"height:0.6667em;vertical-align:-0.0833em;",[572,2573,661],{"className":2574},[615,616],[572,2576],{"className":2577,"style":2516},[726],[572,2579,1843],{"className":2580},[2520],[572,2582],{"className":2583,"style":2516},[726],[572,2585,2587,2590,2593,2596,2599],{"className":2586},[606],[572,2588],{"className":2589,"style":1243},[610],[572,2591,1811],{"className":2592},[615],[572,2594],{"className":2595,"style":727},[726],[572,2597,865],{"className":2598},[731],[572,2600],{"className":2601,"style":727},[726],[572,2603,2605,2608],{"className":2604},[606],[572,2606],{"className":2607,"style":901},[610],[572,2609,869],{"className":2610},[615],". Der Definitionsbereich ist also ",[572,2613,2615,2633],{"className":2614},[575],[572,2616,2618],{"className":2617},[579],[581,2619,2620],{"xmlns":583},[585,2621,2622,2630],{},[588,2623,2624,2626,2628],{},[591,2625,661],{},[697,2627,865],{},[867,2629,1811],{},[595,2631,2632],{"encoding":597},"x > 2",[572,2634,2636,2654],{"className":2635,"ariaHidden":602},[601],[572,2637,2639,2642,2645,2648,2651],{"className":2638},[606],[572,2640],{"className":2641,"style":882},[610],[572,2643,661],{"className":2644},[615,616],[572,2646],{"className":2647,"style":727},[726],[572,2649,865],{"className":2650},[731],[572,2652],{"className":2653,"style":727},[726],[572,2655,2657,2660],{"className":2656},[606],[572,2658],{"className":2659,"style":901},[610],[572,2661,1811],{"className":2662},[615],[559,2664,2666],{"id":2665},"typische-fehler","Typische Fehler",[843,2668,2669,2808,3210],{},[846,2670,2671,2672,1038,2756,2807],{},"Null oder negative Zahlen einsetzen: ",[572,2673,2675,2699],{"className":2674},[575],[572,2676,2678],{"className":2677},[579],[581,2679,2680],{"xmlns":583},[585,2681,2682,2696],{},[588,2683,2684,2694],{},[1314,2685,2686,2692],{},[588,2687,2688,2690],{},[591,2689,1320],{},[697,2691,1308],{},[867,2693,1811],{},[867,2695,869],{},[595,2697,2698],{"encoding":597},"\\log_2 0",[572,2700,2702],{"className":2701,"ariaHidden":602},[601],[572,2703,2705,2708,2750,2753],{"className":2704},[606],[572,2706],{"className":2707,"style":1366},[610],[572,2709,2711,2716],{"className":2710},[1343],[572,2712,1373,2714],{"className":2713},[1343],[572,2715,1377],{"style":1376},[572,2717,2719],{"className":2718},[750],[572,2720,2722,2742],{"className":2721},[754,1384],[572,2723,2725,2739],{"className":2724},[758],[572,2726,2728],{"className":2727,"style":1522},[762],[572,2729,2730,2733],{"style":1394},[572,2731],{"className":2732,"style":771},[770],[572,2734,2736],{"className":2735},[775,776,777,778],[572,2737,1811],{"className":2738},[615,778],[572,2740,1408],{"className":2741},[1407],[572,2743,2745],{"className":2744},[758],[572,2746,2748],{"className":2747,"style":1415},[762],[572,2749],{},[572,2751],{"className":2752,"style":1347},[726],[572,2754,869],{"className":2755},[615],[572,2757,2759,2783],{"className":2758},[575],[572,2760,2762],{"className":2761},[579],[581,2763,2764],{"xmlns":583},[585,2765,2766,2780],{},[588,2767,2768,2770,2772,2774,2776,2778],{},[591,2769,1305],{},[697,2771,1308],{},[697,2773,984],{"stretchy":983},[697,2775,1843],{},[867,2777,1819],{},[697,2779,995],{"stretchy":983},[595,2781,2782],{"encoding":597},"\\ln(-3)",[572,2784,2786],{"className":2785,"ariaHidden":602},[601],[572,2787,2789,2792,2795,2798,2801,2804],{"className":2788},[606],[572,2790],{"className":2791,"style":1008},[610],[572,2793,1305],{"className":2794},[1343],[572,2796,984],{"className":2797},[1012],[572,2799,1843],{"className":2800},[615],[572,2802,1819],{"className":2803},[615],[572,2805,995],{"className":2806},[1037]," gibt es nicht.",[846,2809,2810,2811,3025,3026,838],{},"Den Logarithmus einer Summe aufteilen: ",[572,2812,2814,2866],{"className":2813},[575],[572,2815,2817],{"className":2816},[579],[581,2818,2819],{"xmlns":583},[585,2820,2821,2863],{},[588,2822,2823,2833,2835,2837,2840,2842,2844,2846,2856,2859,2861],{},[1314,2824,2825,2831],{},[588,2826,2827,2829],{},[591,2828,1320],{},[697,2830,1308],{},[867,2832,1811],{},[697,2834,984],{"stretchy":983},[867,2836,1814],{},[697,2838,2839],{},"+",[867,2841,1814],{},[697,2843,995],{"stretchy":983},[697,2845,800],{},[1314,2847,2848,2854],{},[588,2849,2850,2852],{},[591,2851,1320],{},[697,2853,1308],{},[867,2855,1811],{},[867,2857,2858],{},"16",[697,2860,800],{},[867,2862,2218],{},[595,2864,2865],{"encoding":597},"\\log_2(8 + 8) = \\log_2 16 = 4",[572,2867,2869,2932,2953,3016],{"className":2868,"ariaHidden":602},[601],[572,2870,2872,2875,2917,2920,2923,2926,2929],{"className":2871},[606],[572,2873],{"className":2874,"style":1008},[610],[572,2876,2878,2883],{"className":2877},[1343],[572,2879,1373,2881],{"className":2880},[1343],[572,2882,1377],{"style":1376},[572,2884,2886],{"className":2885},[750],[572,2887,2889,2909],{"className":2888},[754,1384],[572,2890,2892,2906],{"className":2891},[758],[572,2893,2895],{"className":2894,"style":1522},[762],[572,2896,2897,2900],{"style":1394},[572,2898],{"className":2899,"style":771},[770],[572,2901,2903],{"className":2902},[775,776,777,778],[572,2904,1811],{"className":2905},[615,778],[572,2907,1408],{"className":2908},[1407],[572,2910,2912],{"className":2911},[758],[572,2913,2915],{"className":2914,"style":1415},[762],[572,2916],{},[572,2918,984],{"className":2919},[1012],[572,2921,1814],{"className":2922},[615],[572,2924],{"className":2925,"style":2516},[726],[572,2927,2839],{"className":2928},[2520],[572,2930],{"className":2931,"style":2516},[726],[572,2933,2935,2938,2941,2944,2947,2950],{"className":2934},[606],[572,2936],{"className":2937,"style":1008},[610],[572,2939,1814],{"className":2940},[615],[572,2942,995],{"className":2943},[1037],[572,2945],{"className":2946,"style":727},[726],[572,2948,800],{"className":2949},[731],[572,2951],{"className":2952,"style":727},[726],[572,2954,2956,2959,3001,3004,3007,3010,3013],{"className":2955},[606],[572,2957],{"className":2958,"style":1366},[610],[572,2960,2962,2967],{"className":2961},[1343],[572,2963,1373,2965],{"className":2964},[1343],[572,2966,1377],{"style":1376},[572,2968,2970],{"className":2969},[750],[572,2971,2973,2993],{"className":2972},[754,1384],[572,2974,2976,2990],{"className":2975},[758],[572,2977,2979],{"className":2978,"style":1522},[762],[572,2980,2981,2984],{"style":1394},[572,2982],{"className":2983,"style":771},[770],[572,2985,2987],{"className":2986},[775,776,777,778],[572,2988,1811],{"className":2989},[615,778],[572,2991,1408],{"className":2992},[1407],[572,2994,2996],{"className":2995},[758],[572,2997,2999],{"className":2998,"style":1415},[762],[572,3000],{},[572,3002],{"className":3003,"style":1347},[726],[572,3005,2858],{"className":3006},[615],[572,3008],{"className":3009,"style":727},[726],[572,3011,800],{"className":3012},[731],[572,3014],{"className":3015,"style":727},[726],[572,3017,3019,3022],{"className":3018},[606],[572,3020],{"className":3021,"style":901},[610],[572,3023,2218],{"className":3024},[615],", nicht ",[572,3027,3029,3072],{"className":3028},[575],[572,3030,3032],{"className":3031},[579],[581,3033,3034],{"xmlns":583},[585,3035,3036,3069],{},[588,3037,3038,3048,3050,3052,3062,3064,3066],{},[1314,3039,3040,3046],{},[588,3041,3042,3044],{},[591,3043,1320],{},[697,3045,1308],{},[867,3047,1811],{},[867,3049,1814],{},[697,3051,2839],{},[1314,3053,3054,3060],{},[588,3055,3056,3058],{},[591,3057,1320],{},[697,3059,1308],{},[867,3061,1811],{},[867,3063,1814],{},[697,3065,800],{},[867,3067,3068],{},"6",[595,3070,3071],{"encoding":597},"\\log_2 8 + \\log_2 8 = 6",[572,3073,3075,3138,3201],{"className":3074,"ariaHidden":602},[601],[572,3076,3078,3081,3123,3126,3129,3132,3135],{"className":3077},[606],[572,3079],{"className":3080,"style":1366},[610],[572,3082,3084,3089],{"className":3083},[1343],[572,3085,1373,3087],{"className":3086},[1343],[572,3088,1377],{"style":1376},[572,3090,3092],{"className":3091},[750],[572,3093,3095,3115],{"className":3094},[754,1384],[572,3096,3098,3112],{"className":3097},[758],[572,3099,3101],{"className":3100,"style":1522},[762],[572,3102,3103,3106],{"style":1394},[572,3104],{"className":3105,"style":771},[770],[572,3107,3109],{"className":3108},[775,776,777,778],[572,3110,1811],{"className":3111},[615,778],[572,3113,1408],{"className":3114},[1407],[572,3116,3118],{"className":3117},[758],[572,3119,3121],{"className":3120,"style":1415},[762],[572,3122],{},[572,3124],{"className":3125,"style":1347},[726],[572,3127,1814],{"className":3128},[615],[572,3130],{"className":3131,"style":2516},[726],[572,3133,2839],{"className":3134},[2520],[572,3136],{"className":3137,"style":2516},[726],[572,3139,3141,3144,3186,3189,3192,3195,3198],{"className":3140},[606],[572,3142],{"className":3143,"style":1366},[610],[572,3145,3147,3152],{"className":3146},[1343],[572,3148,1373,3150],{"className":3149},[1343],[572,3151,1377],{"style":1376},[572,3153,3155],{"className":3154},[750],[572,3156,3158,3178],{"className":3157},[754,1384],[572,3159,3161,3175],{"className":3160},[758],[572,3162,3164],{"className":3163,"style":1522},[762],[572,3165,3166,3169],{"style":1394},[572,3167],{"className":3168,"style":771},[770],[572,3170,3172],{"className":3171},[775,776,777,778],[572,3173,1811],{"className":3174},[615,778],[572,3176,1408],{"className":3177},[1407],[572,3179,3181],{"className":3180},[758],[572,3182,3184],{"className":3183,"style":1415},[762],[572,3185],{},[572,3187],{"className":3188,"style":1347},[726],[572,3190,1814],{"className":3191},[615],[572,3193],{"className":3194,"style":727},[726],[572,3196,800],{"className":3197},[731],[572,3199],{"className":3200,"style":727},[726],[572,3202,3204,3207],{"className":3203},[606],[572,3205],{"className":3206,"style":901},[610],[572,3208,3068],{"className":3209},[615],[846,3211,3212,3213,3263,3264,838],{},"Beim Definitionsbereich nur ",[572,3214,3216,3233],{"className":3215},[575],[572,3217,3219],{"className":3218},[579],[581,3220,3221],{"xmlns":583},[585,3222,3223,3231],{},[588,3224,3225,3227,3229],{},[591,3226,661],{},[697,3228,865],{},[867,3230,869],{},[595,3232,872],{"encoding":597},[572,3234,3236,3254],{"className":3235,"ariaHidden":602},[601],[572,3237,3239,3242,3245,3248,3251],{"className":3238},[606],[572,3240],{"className":3241,"style":882},[610],[572,3243,661],{"className":3244},[615,616],[572,3246],{"className":3247,"style":727},[726],[572,3249,865],{"className":3250},[731],[572,3252],{"className":3253,"style":727},[726],[572,3255,3257,3260],{"className":3256},[606],[572,3258],{"className":3259,"style":901},[610],[572,3261,869],{"className":3262},[615]," notieren, obwohl das Argument verschoben ist, wie bei 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