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Wurzel:",[579,1680,1682],{"className":1681},[859],[579,1683,1685,1742],{"className":1684},[582],[579,1686,1688],{"className":1687},[586],[588,1689,1690],{"xmlns":590,"display":868},[592,1691,1692,1739],{},[595,1693,1694,1697,1699,1703,1705,1707,1709,1725,1727,1733,1735,1737],{},[601,1695,1696],{},"ln",[605,1698,883],{},[598,1700,1701],{},[601,1702,1212],{},[605,1704,607],{},[601,1706,1696],{},[605,1708,883],{},[595,1710,1711,1713,1723],{},[605,1712,890],{"fence":632},[609,1714,1715,1717],{},[601,1716,1212],{},[614,1718,1719,1721],{},[617,1720,619],{},[617,1722,622],{},[605,1724,901],{"fence":632},[605,1726,607],{},[614,1728,1729,1731],{},[617,1730,619],{},[617,1732,622],{},[601,1734,1696],{},[605,1736,883],{},[601,1738,1212],{},[624,1740,1741],{"encoding":626},"\\ln \\sqrt{x} = \\ln \\left(x^{\\frac{1}{2}}\\right) = \\frac{1}{2} \\ln x",[579,1743,1745,1817,1954],{"className":1744,"ariaHidden":632},[631],[579,1746,1748,1752,1755,1758,1808,1811,1814],{"className":1747},[636],[579,1749],{"className":1750,"style":1751},[640],"height:1.04em;vertical-align:-0.1908em;",[579,1753,1696],{"className":1754},[951],[579,1756],{"className":1757,"style":1001},[719],[579,1759,1761],{"className":1760},[645,646],[579,1762,1764,1799],{"className":1763},[650,651],[579,1765,1767,1796],{"className":1766},[655],[579,1768,1771,1783],{"className":1769,"style":1770},[659],"height:0.8492em;",[579,1772,1774,1777],{"className":1773,"style":665},[664],[579,1775],{"className":1776,"style":670},[669],[579,1778,1780],{"className":1779,"style":674},[645],[579,1781,1212],{"className":1782},[645,678],[579,1784,1786,1789],{"style":1785},"top:-2.8092em;",[579,1787],{"className":1788,"style":670},[669],[579,1790,1792],{"className":1791,"style":689},[688],[691,1793,1794],{"xmlns":693,"width":694,"height":695,"viewBox":696,"preserveAspectRatio":697},[699,1795],{"d":701},[579,1797,706],{"className":1798},[705],[579,1800,1802],{"className":1801},[655],[579,1803,1806],{"className":1804,"style":1805},[659],"height:0.1908em;",[579,1807],{},[579,1809],{"className":1810,"style":720},[719],[579,1812,607],{"className":1813},[724],[579,1815],{"className":1816,"style":720},[719],[579,1818,1820,1824,1827,1830,1945,1948,1951],{"className":1819},[636],[579,1821],{"className":1822,"style":1823},[640],"height:1.8em;vertical-align:-0.65em;",[579,1825,1696],{"className":1826},[951],[579,1828],{"className":1829,"style":1001},[719],[579,1831,1833,1840,1939],{"className":1832},[1005],[579,1834,1836],{"className":1835,"style":1010},[776,1009],[579,1837,890],{"className":1838},[1014,1839],"size2",[579,1841,1843,1846],{"className":1842},[645],[579,1844,1212],{"className":1845},[645,678],[579,1847,1849],{"className":1848},[744],[579,1850,1852],{"className":1851},[650],[579,1853,1855],{"className":1854},[655],[579,1856,1859],{"className":1857,"style":1858},[659],"height:1.004em;",[579,1860,1862,1865],{"style":1861},"top:-3.413em;margin-right:0.05em;",[579,1863],{"className":1864,"style":670},[669],[579,1866,1868],{"className":1867},[763,764,765,766],[579,1869,1871],{"className":1870},[645,766],[579,1872,1874,1877,1936],{"className":1873},[645,766],[579,1875],{"className":1876},[776,777,763,778,779],[579,1878,1880],{"className":1879},[614],[579,1881,1883,1928],{"className":1882},[650,651],[579,1884,1886,1925],{"className":1885},[655],[579,1887,1889,1903,1911],{"className":1888,"style":792},[659],[579,1890,1891,1894],{"style":795},[579,1892],{"className":1893,"style":670},[669],[579,1895,1897],{"className":1896},[763,778,802,766],[579,1898,1900],{"className":1899},[645,766],[579,1901,622],{"className":1902},[645,766],[579,1904,1905,1908],{"style":811},[579,1906],{"className":1907,"style":670},[669],[579,1909],{"className":1910,"style":819},[818,766],[579,1912,1913,1916],{"style":822},[579,1914],{"className":1915,"style":670},[669],[579,1917,1919],{"className":1918},[763,778,802,766],[579,1920,1922],{"className":1921},[645,766],[579,1923,619],{"className":1924},[645,766],[579,1926,706],{"className":1927},[705],[579,1929,1931],{"className":1930},[655],[579,1932,1934],{"className":1933,"style":844},[659],[579,1935],{},[579,1937],{"className":1938},[850,777,763,778,779],[579,1940,1942],{"className":1941,"style":1010},[850,1009],[579,1943,901],{"className":1944},[1014,1839],[579,1946],{"className":1947,"style":720},[719],[579,1949,607],{"className":1950},[724],[579,1952],{"className":1953,"style":720},[719],[579,1955,1957,1961,2024,2027,2030,2033],{"className":1956},[636],[579,1958],{"className":1959,"style":1960},[640],"height:2.0074em;vertical-align:-0.686em;",[579,1962,1964,1967,2021],{"className":1963},[645],[579,1965],{"className":1966},[776,777],[579,1968,1970],{"className":1969},[614],[579,1971,1973,2012],{"className":1972},[650,651],[579,1974,1976,2009],{"className":1975},[655],[579,1977,1979,1990,1998],{"className":1978,"style":1587},[659],[579,1980,1981,1984],{"style":1590},[579,1982],{"className":1983,"style":670},[669],[579,1985,1987],{"className":1986},[645],[579,1988,622],{"className":1989},[645],[579,1991,1992,1995],{"style":1610},[579,1993],{"className":1994,"style":670},[669],[579,1996],{"className":1997,"style":1617},[818],[579,1999,2000,2003],{"style":1620},[579,2001],{"className":2002,"style":670},[669],[579,2004,2006],{"className":2005},[645],[579,2007,619],{"className":2008},[645],[579,2010,706],{"className":2011},[705],[579,2013,2015],{"className":2014},[655],[579,2016,2019],{"className":2017,"style":2018},[659],"height:0.686em;",[579,2020],{},[579,2022],{"className":2023},[850,777],[579,2025],{"className":2026,"style":1001},[719],[579,2028,1696],{"className":2029},[951],[579,2031],{"className":2032,"style":1001},[719],[579,2034,1212],{"className":2035},[645,678],[558,2037,2039],{"id":2038},"typische-fehler","Typische Fehler",[2041,2042,2043,2325,2739],"ul",{},[2044,2045,2046,2047,2324],"li",{},"Den Logarithmus potenzieren: ",[579,2048,2050,2106],{"className":2049},[582],[579,2051,2053],{"className":2052},[586],[588,2054,2055],{"xmlns":590},[592,2056,2057,2103],{},[595,2058,2059,2083,2087,2089,2091,2101],{},[609,2060,2061,2080],{},[595,2062,2063,2065,2076,2078],{},[605,2064,890],{"fence":632},[874,2066,2067,2073],{},[595,2068,2069,2071],{},[601,2070,880],{},[605,2072,883],{},[601,2074,2075],{},"a",[601,2077,603],{},[605,2079,901],{"fence":632},[601,2081,2082],{},"r",[605,2084,2086],{"mathvariant":2085},"normal","≠",[601,2088,2082],{},[605,2090,908],{},[874,2092,2093,2099],{},[595,2094,2095,2097],{},[601,2096,880],{},[605,2098,883],{},[601,2100,2075],{},[601,2102,603],{},[624,2104,2105],{"encoding":626},"\\left(\\log_a u\\right)^r \\neq r \\cdot \\log_a u",[579,2107,2109,2252,2270],{"className":2108,"ariaHidden":632},[631],[579,2110,2112,2116,2203,2206,2249],{"className":2111},[636],[579,2113],{"className":2114,"style":2115},[640],"height:1.0543em;vertical-align:-0.25em;",[579,2117,2119,2177],{"className":2118},[1005],[579,2120,2122,2125,2168,2171,2174],{"className":2121},[1005],[579,2123,890],{"className":2124,"style":1010},[776,1009],[579,2126,2128,2133],{"className":2127},[951],[579,2129,955,2131],{"className":2130},[951],[579,2132,959],{"style":958},[579,2134,2136],{"className":2135},[744],[579,2137,2139,2160],{"className":2138},[650,651],[579,2140,2142,2157],{"className":2141},[655],[579,2143,2146],{"className":2144,"style":2145},[659],"height:0.0573em;",[579,2147,2148,2151],{"style":975},[579,2149],{"className":2150,"style":979},[669],[579,2152,2154],{"className":2153},[763,764,765,766],[579,2155,2075],{"className":2156},[645,678,766],[579,2158,706],{"className":2159},[705],[579,2161,2163],{"className":2162},[655],[579,2164,2166],{"className":2165,"style":995},[659],[579,2167],{},[579,2169],{"className":2170,"style":1001},[719],[579,2172,603],{"className":2173},[645,678],[579,2175,901],{"className":2176,"style":1010},[850,1009],[579,2178,2180],{"className":2179},[744],[579,2181,2183],{"className":2182},[650],[579,2184,2186],{"className":2185},[655],[579,2187,2190],{"className":2188,"style":2189},[659],"height:0.8043em;",[579,2191,2193,2196],{"style":2192},"top:-3.2029em;margin-right:0.05em;",[579,2194],{"className":2195,"style":979},[669],[579,2197,2199],{"className":2198},[763,764,765,766],[579,2200,2082],{"className":2201,"style":2202},[645,678,766],"margin-right:0.0278em;",[579,2204],{"className":2205,"style":720},[719],[579,2207,2209,2242,2246],{"className":2208},[724],[579,2210,2212],{"className":2211},[724],[579,2213,2216],{"className":2214},[645,2215],"vbox",[579,2217,2220],{"className":2218},[2219],"thinbox",[579,2221,2224,2227,2238],{"className":2222},[2223],"rlap",[579,2225],{"className":2226,"style":1447},[640],[579,2228,2231],{"className":2229},[2230],"inner",[579,2232,2234],{"className":2233},[645],[579,2235,2237],{"className":2236},[724],"",[579,2239],{"className":2240},[2241],"fix",[579,2243],{"className":2244},[719,2245],"nobreak",[579,2247,607],{"className":2248},[724],[579,2250],{"className":2251,"style":720},[719],[579,2253,2255,2258,2261,2264,2267],{"className":2254},[636],[579,2256],{"className":2257,"style":1480},[640],[579,2259,2082],{"className":2260,"style":2202},[645,678],[579,2262],{"className":2263,"style":1074},[719],[579,2265,908],{"className":2266},[1078],[579,2268],{"className":2269,"style":1074},[719],[579,2271,2273,2276,2318,2321],{"className":2272},[636],[579,2274],{"className":2275,"style":1088},[640],[579,2277,2279,2284],{"className":2278},[951],[579,2280,955,2282],{"className":2281},[951],[579,2283,959],{"style":958},[579,2285,2287],{"className":2286},[744],[579,2288,2290,2310],{"className":2289},[650,651],[579,2291,2293,2307],{"className":2292},[655],[579,2294,2296],{"className":2295,"style":2145},[659],[579,2297,2298,2301],{"style":975},[579,2299],{"className":2300,"style":979},[669],[579,2302,2304],{"className":2303},[763,764,765,766],[579,2305,2075],{"className":2306},[645,678,766],[579,2308,706],{"className":2309},[705],[579,2311,2313],{"className":2312},[655],[579,2314,2316],{"className":2315,"style":995},[659],[579,2317],{},[579,2319],{"className":2320,"style":1001},[719],[579,2322,603],{"className":2323},[645,678],".",[2044,2326,2327,2328,2633,2634,2324],{},"Einen Faktor vor der Potenz mitnehmen: ",[579,2329,2331,2398],{"className":2330},[582],[579,2332,2334],{"className":2333},[586],[588,2335,2336],{"xmlns":590},[592,2337,2338,2395],{},[595,2339,2340,2350,2364,2366,2376,2378,2381,2383,2393],{},[874,2341,2342,2348],{},[595,2343,2344,2346],{},[601,2345,880],{},[605,2347,883],{},[601,2349,2075],{},[595,2351,2352,2354,2356,2362],{},[605,2353,890],{"fence":632},[617,2355,929],{},[609,2357,2358,2360],{},[601,2359,603],{},[617,2361,622],{},[605,2363,901],{"fence":632},[605,2365,607],{},[874,2367,2368,2374],{},[595,2369,2370,2372],{},[601,2371,880],{},[605,2373,883],{},[601,2375,2075],{},[617,2377,929],{},[605,2379,2380],{},"+",[617,2382,622],{},[874,2384,2385,2391],{},[595,2386,2387,2389],{},[601,2388,880],{},[605,2390,883],{},[601,2392,2075],{},[601,2394,603],{},[624,2396,2397],{"encoding":626},"\\log_a \\left(3 u^2\\right) = \\log_a 3 + 2 \\log_a u",[579,2399,2401,2510,2573],{"className":2400,"ariaHidden":632},[631],[579,2402,2404,2408,2450,2453,2501,2504,2507],{"className":2403},[636],[579,2405],{"className":2406,"style":2407},[640],"height:1.2em;vertical-align:-0.35em;",[579,2409,2411,2416],{"className":2410},[951],[579,2412,955,2414],{"className":2413},[951],[579,2415,959],{"style":958},[579,2417,2419],{"className":2418},[744],[579,2420,2422,2442],{"className":2421},[650,651],[579,2423,2425,2439],{"className":2424},[655],[579,2426,2428],{"className":2427,"style":2145},[659],[579,2429,2430,2433],{"style":975},[579,2431],{"className":2432,"style":979},[669],[579,2434,2436],{"className":2435},[763,764,765,766],[579,2437,2075],{"className":2438},[645,678,766],[579,2440,706],{"className":2441},[705],[579,2443,2445],{"className":2444},[655],[579,2446,2448],{"className":2447,"style":995},[659],[579,2449],{},[579,2451],{"className":2452,"style":1001},[719],[579,2454,2456,2462,2465,2495],{"className":2455},[1005],[579,2457,2459],{"className":2458,"style":1010},[776,1009],[579,2460,890],{"className":2461},[1014,802],[579,2463,929],{"className":2464},[645],[579,2466,2468,2471],{"className":2467},[645],[579,2469,603],{"className":2470},[645,678],[579,2472,2474],{"className":2473},[744],[579,2475,2477],{"className":2476},[650],[579,2478,2480],{"className":2479},[655],[579,2481,2484],{"className":2482,"style":2483},[659],"height:0.8141em;",[579,2485,2486,2489],{"style":1251},[579,2487],{"className":2488,"style":979},[669],[579,2490,2492],{"className":2491},[763,764,765,766],[579,2493,622],{"className":2494},[645,766],[579,2496,2498],{"className":2497,"style":1010},[850,1009],[579,2499,901],{"className":2500},[1014,802],[579,2502],{"className":2503,"style":720},[719],[579,2505,607],{"className":2506},[724],[579,2508],{"className":2509,"style":720},[719],[579,2511,2513,2516,2558,2561,2564,2567,2570],{"className":2512},[636],[579,2514],{"className":2515,"style":1088},[640],[579,2517,2519,2524],{"className":2518},[951],[579,2520,955,2522],{"className":2521},[951],[579,2523,959],{"style":958},[579,2525,2527],{"className":2526},[744],[579,2528,2530,2550],{"className":2529},[650,651],[579,2531,2533,2547],{"className":2532},[655],[579,2534,2536],{"className":2535,"style":2145},[659],[579,2537,2538,2541],{"style":975},[579,2539],{"className":2540,"style":979},[669],[579,2542,2544],{"className":2543},[763,764,765,766],[579,2545,2075],{"className":2546},[645,678,766],[579,2548,706],{"className":2549},[705],[579,2551,2553],{"className":2552},[655],[579,2554,2556],{"className":2555,"style":995},[659],[579,2557],{},[579,2559],{"className":2560,"style":1001},[719],[579,2562,929],{"className":2563},[645],[579,2565],{"className":2566,"style":1074},[719],[579,2568,2380],{"className":2569},[1078],[579,2571],{"className":2572,"style":1074},[719],[579,2574,2576,2579,2582,2585,2627,2630],{"className":2575},[636],[579,2577],{"className":2578,"style":1088},[640],[579,2580,622],{"className":2581},[645],[579,2583],{"className":2584,"style":1001},[719],[579,2586,2588,2593],{"className":2587},[951],[579,2589,955,2591],{"className":2590},[951],[579,2592,959],{"style":958},[579,2594,2596],{"className":2595},[744],[579,2597,2599,2619],{"className":2598},[650,651],[579,2600,2602,2616],{"className":2601},[655],[579,2603,2605],{"className":2604,"style":2145},[659],[579,2606,2607,2610],{"style":975},[579,2608],{"className":2609,"style":979},[669],[579,2611,2613],{"className":2612},[763,764,765,766],[579,2614,2075],{"className":2615},[645,678,766],[579,2617,706],{"className":2618},[705],[579,2620,2622],{"className":2621},[655],[579,2623,2625],{"className":2624,"style":995},[659],[579,2626],{},[579,2628],{"className":2629,"style":1001},[719],[579,2631,603],{"className":2632},[645,678],", nicht ",[579,2635,2637,2670],{"className":2636},[582],[579,2638,2640],{"className":2639},[586],[588,2641,2642],{"xmlns":590},[592,2643,2644,2667],{},[595,2645,2646,2648,2658,2661,2663,2665],{},[617,2647,622],{},[874,2649,2650,2656],{},[595,2651,2652,2654],{},[601,2653,880],{},[605,2655,883],{},[601,2657,2075],{},[605,2659,890],{"stretchy":2660},"false",[617,2662,929],{},[601,2664,603],{},[605,2666,901],{"stretchy":2660},[624,2668,2669],{"encoding":626},"2 \\log_a (3u)",[579,2671,2673],{"className":2672,"ariaHidden":632},[631],[579,2674,2676,2679,2682,2685,2727,2730,2733,2736],{"className":2675},[636],[579,2677],{"className":2678,"style":1383},[640],[579,2680,622],{"className":2681},[645],[579,2683],{"className":2684,"style":1001},[719],[579,2686,2688,2693],{"className":2687},[951],[579,2689,955,2691],{"className":2690},[951],[579,2692,959],{"style":958},[579,2694,2696],{"className":2695},[744],[579,2697,2699,2719],{"className":2698},[650,651],[579,2700,2702,2716],{"className":2701},[655],[579,2703,2705],{"className":2704,"style":2145},[659],[579,2706,2707,2710],{"style":975},[579,2708],{"className":2709,"style":979},[669],[579,2711,2713],{"className":2712},[763,764,765,766],[579,2714,2075],{"className":2715},[645,678,766],[579,2717,706],{"className":2718},[705],[579,2720,2722],{"className":2721},[655],[579,2723,2725],{"className":2724,"style":995},[659],[579,2726],{},[579,2728,890],{"className":2729},[776],[579,2731,929],{"className":2732},[645],[579,2734,603],{"className":2735},[645,678],[579,2737,901],{"className":2738},[850],[2044,2740,2741,2742,2770,2771,2633,3007,3111,3112,3140,3141,2324],{},"Die Regel auf ein negatives ",[579,2743,2745,2758],{"className":2744},[582],[579,2746,2748],{"className":2747},[586],[588,2749,2750],{"xmlns":590},[592,2751,2752,2756],{},[595,2753,2754],{},[601,2755,603],{},[624,2757,603],{"encoding":626},[579,2759,2761],{"className":2760,"ariaHidden":632},[631],[579,2762,2764,2767],{"className":2763},[636],[579,2765],{"className":2766,"style":1549},[640],[579,2768,603],{"className":2769},[645,678]," anwenden: ",[579,2772,2774,2831],{"className":2773},[582],[579,2775,2777],{"className":2776},[586],[588,2778,2779],{"xmlns":590},[592,2780,2781,2828],{},[595,2782,2783,2793,2812,2814,2816,2826],{},[874,2784,2785,2791],{},[595,2786,2787,2789],{},[601,2788,880],{},[605,2790,883],{},[601,2792,2075],{},[595,2794,2795,2797,2799,2802,2804,2810],{},[605,2796,890],{"fence":632},[605,2798,890],{"stretchy":2660},[605,2800,2801],{},"−",[617,2803,622],{},[609,2805,2806,2808],{},[605,2807,901],{"stretchy":2660},[617,2809,622],{},[605,2811,901],{"fence":632},[605,2813,607],{},[617,2815,622],{},[874,2817,2818,2824],{},[595,2819,2820,2822],{},[601,2821,880],{},[605,2823,883],{},[601,2825,2075],{},[617,2827,622],{},[624,2829,2830],{"encoding":626},"\\log_a \\left((-2)^2\\right) = 2 \\log_a 2",[579,2832,2834,2947],{"className":2833,"ariaHidden":632},[631],[579,2835,2837,2840,2882,2885,2938,2941,2944],{"className":2836},[636],[579,2838],{"className":2839,"style":2407},[640],[579,2841,2843,2848],{"className":2842},[951],[579,2844,955,2846],{"className":2845},[951],[579,2847,959],{"style":958},[579,2849,2851],{"className":2850},[744],[579,2852,2854,2874],{"className":2853},[650,651],[579,2855,2857,2871],{"className":2856},[655],[579,2858,2860],{"className":2859,"style":2145},[659],[579,2861,2862,2865],{"style":975},[579,2863],{"className":2864,"style":979},[669],[579,2866,2868],{"className":2867},[763,764,765,766],[579,2869,2075],{"className":2870},[645,678,766],[579,2872,706],{"className":2873},[705],[579,2875,2877],{"className":2876},[655],[579,2878,2880],{"className":2879,"style":995},[659],[579,2881],{},[579,2883],{"className":2884,"style":1001},[719],[579,2886,2888,2894,2897,2900,2903,2932],{"className":2887},[1005],[579,2889,2891],{"className":2890,"style":1010},[776,1009],[579,2892,890],{"className":2893},[1014,802],[579,2895,890],{"className":2896},[776],[579,2898,2801],{"className":2899},[645],[579,2901,622],{"className":2902},[645],[579,2904,2906,2909],{"className":2905},[850],[579,2907,901],{"className":2908},[850],[579,2910,2912],{"className":2911},[744],[579,2913,2915],{"className":2914},[650],[579,2916,2918],{"className":2917},[655],[579,2919,2921],{"className":2920,"style":2483},[659],[579,2922,2923,2926],{"style":1251},[579,2924],{"className":2925,"style":979},[669],[579,2927,2929],{"className":2928},[763,764,765,766],[579,2930,622],{"className":2931},[645,766],[579,2933,2935],{"className":2934,"style":1010},[850,1009],[579,2936,901],{"className":2937},[1014,802],[579,2939],{"className":2940,"style":720},[719],[579,2942,607],{"className":2943},[724],[579,2945],{"className":2946,"style":720},[719],[579,2948,2950,2953,2956,2959,3001,3004],{"className":2949},[636],[579,2951],{"className":2952,"style":1088},[640],[579,2954,622],{"className":2955},[645],[579,2957],{"className":2958,"style":1001},[719],[579,2960,2962,2967],{"className":2961},[951],[579,2963,955,2965],{"className":2964},[951],[579,2966,959],{"style":958},[579,2968,2970],{"className":2969},[744],[579,2971,2973,2993],{"className":2972},[650,651],[579,2974,2976,2990],{"className":2975},[655],[579,2977,2979],{"className":2978,"style":2145},[659],[579,2980,2981,2984],{"style":975},[579,2982],{"className":2983,"style":979},[669],[579,2985,2987],{"className":2986},[763,764,765,766],[579,2988,2075],{"className":2989},[645,678,766],[579,2991,706],{"className":2992},[705],[579,2994,2996],{"className":2995},[655],[579,2997,2999],{"className":2998,"style":995},[659],[579,3000],{},[579,3002],{"className":3003,"style":1001},[719],[579,3005,622],{"className":3006},[645],[579,3008,3010,3042],{"className":3009},[582],[579,3011,3013],{"className":3012},[586],[588,3014,3015],{"xmlns":590},[592,3016,3017,3039],{},[595,3018,3019,3021,3031,3033,3035,3037],{},[617,3020,622],{},[874,3022,3023,3029],{},[595,3024,3025,3027],{},[601,3026,880],{},[605,3028,883],{},[601,3030,2075],{},[605,3032,890],{"stretchy":2660},[605,3034,2801],{},[617,3036,622],{},[605,3038,901],{"stretchy":2660},[624,3040,3041],{"encoding":626},"2 \\log_a (-2)",[579,3043,3045],{"className":3044,"ariaHidden":632},[631],[579,3046,3048,3051,3054,3057,3099,3102,3105,3108],{"className":3047},[636],[579,3049],{"className":3050,"style":1383},[640],[579,3052,622],{"className":3053},[645],[579,3055],{"className":3056,"style":1001},[719],[579,3058,3060,3065],{"className":3059},[951],[579,3061,955,3063],{"className":3062},[951],[579,3064,959],{"style":958},[579,3066,3068],{"className":3067},[744],[579,3069,3071,3091],{"className":3070},[650,651],[579,3072,3074,3088],{"className":3073},[655],[579,3075,3077],{"className":3076,"style":2145},[659],[579,3078,3079,3082],{"style":975},[579,3080],{"className":3081,"style":979},[669],[579,3083,3085],{"className":3084},[763,764,765,766],[579,3086,2075],{"className":3087},[645,678,766],[579,3089,706],{"className":3090},[705],[579,3092,3094],{"className":3093},[655],[579,3095,3097],{"className":3096,"style":995},[659],[579,3098],{},[579,3100,890],{"className":3101},[776],[579,3103,2801],{"className":3104},[645],[579,3106,622],{"className":3107},[645],[579,3109,901],{"className":3110},[850],". Allgemein gilt für gerades ",[579,3113,3115,3128],{"className":3114},[582],[579,3116,3118],{"className":3117},[586],[588,3119,3120],{"xmlns":590},[592,3121,3122,3126],{},[595,3123,3124],{},[601,3125,2082],{},[624,3127,2082],{"encoding":626},[579,3129,3131],{"className":3130,"ariaHidden":632},[631],[579,3132,3134,3137],{"className":3133},[636],[579,3135],{"className":3136,"style":1549},[640],[579,3138,2082],{"className":3139,"style":2202},[645,678],": ",[579,3142,3144,3201],{"className":3143},[582],[579,3145,3147],{"className":3146},[586],[588,3148,3149],{"xmlns":590},[592,3150,3151,3198],{},[595,3152,3153,3163,3175,3177,3179,3181,3191,3194,3196],{},[874,3154,3155,3161],{},[595,3156,3157,3159],{},[601,3158,880],{},[605,3160,883],{},[601,3162,2075],{},[595,3164,3165,3167,3173],{},[605,3166,890],{"fence":632},[609,3168,3169,3171],{},[601,3170,603],{},[601,3172,2082],{},[605,3174,901],{"fence":632},[605,3176,607],{},[601,3178,2082],{},[605,3180,908],{},[874,3182,3183,3189],{},[595,3184,3185,3187],{},[601,3186,880],{},[605,3188,883],{},[601,3190,2075],{},[601,3192,3193],{"mathvariant":2085},"∣",[601,3195,603],{},[601,3197,3193],{"mathvariant":2085},[624,3199,3200],{"encoding":626},"\\log_a \\left(u^r\\right) = r \\cdot \\log_a |u|",[579,3202,3204,3302,3320],{"className":3203,"ariaHidden":632},[631],[579,3205,3207,3210,3252,3255,3293,3296,3299],{"className":3206},[636],[579,3208],{"className":3209,"style":1383},[640],[579,3211,3213,3218],{"className":3212},[951],[579,3214,955,3216],{"className":3215},[951],[579,3217,959],{"style":958},[579,3219,3221],{"className":3220},[744],[579,3222,3224,3244],{"className":3223},[650,651],[579,3225,3227,3241],{"className":3226},[655],[579,3228,3230],{"className":3229,"style":2145},[659],[579,3231,3232,3235],{"style":975},[579,3233],{"className":3234,"style":979},[669],[579,3236,3238],{"className":3237},[763,764,765,766],[579,3239,2075],{"className":3240},[645,678,766],[579,3242,706],{"className":3243},[705],[579,3245,3247],{"className":3246},[655],[579,3248,3250],{"className":3249,"style":995},[659],[579,3251],{},[579,3253],{"className":3254,"style":1001},[719],[579,3256,3258,3261,3290],{"className":3257},[1005],[579,3259,890],{"className":3260,"style":1010},[776,1009],[579,3262,3264,3267],{"className":3263},[645],[579,3265,603],{"className":3266},[645,678],[579,3268,3270],{"className":3269},[744],[579,3271,3273],{"className":3272},[650],[579,3274,3276],{"className":3275},[655],[579,3277,3279],{"className":3278,"style":1230},[659],[579,3280,3281,3284],{"style":1251},[579,3282],{"className":3283,"style":979},[669],[579,3285,3287],{"className":3286},[763,764,765,766],[579,3288,2082],{"className":3289,"style":2202},[645,678,766],[579,3291,901],{"className":3292,"style":1010},[850,1009],[579,3294],{"className":3295,"style":720},[719],[579,3297,607],{"className":3298},[724],[579,3300],{"className":3301,"style":720},[719],[579,3303,3305,3308,3311,3314,3317],{"className":3304},[636],[579,3306],{"className":3307,"style":1480},[640],[579,3309,2082],{"className":3310,"style":2202},[645,678],[579,3312],{"className":3313,"style":1074},[719],[579,3315,908],{"className":3316},[1078],[579,3318],{"className":3319,"style":1074},[719],[579,3321,3323,3326,3368,3371,3374,3377],{"className":3322},[636],[579,3324],{"className":3325,"style":1383},[640],[579,3327,3329,3334],{"className":3328},[951],[579,3330,955,3332],{"className":3331},[951],[579,3333,959],{"style":958},[579,3335,3337],{"className":3336},[744],[579,3338,3340,3360],{"className":3339},[650,651],[579,3341,3343,3357],{"className":3342},[655],[579,3344,3346],{"className":3345,"style":2145},[659],[579,3347,3348,3351],{"style":975},[579,3349],{"className":3350,"style":979},[669],[579,3352,3354],{"className":3353},[763,764,765,766],[579,3355,2075],{"className":3356},[645,678,766],[579,3358,706],{"className":3359},[705],[579,3361,3363],{"className":3362},[655],[579,3364,3366],{"className":3365,"style":995},[659],[579,3367],{},[579,3369],{"className":3370,"style":1001},[719],[579,3372,3193],{"className":3373},[645],[579,3375,603],{"className":3376},[645,678],[579,3378,3193],{"className":3379},[645],{"title":3381,"searchDepth":3382,"depth":3382,"links":3383},"",2,[3384,3385,3386],{"id":560,"depth":3382,"text":561},{"id":854,"depth":3382,"text":855},{"id":2038,"depth":3382,"text":2039},[3388,3391,3393,3396,3398],{"lhs":3389,"rhs":3390},"log(u^r, a)","r * log(u, a)",{"lhs":3392,"rhs":934},"log(8^5, 2)",{"lhs":3394,"rhs":3395},"log10(10) \u002F log10(2)","log(10, 2)",{"lhs":3397,"rhs":1217},"2^(1 \u002F log10(2))",{"lhs":3399,"rhs":3400},"log(sqrt(x))","log(x) \u002F 2","a > 0,\\ a \\neq 1,\\ u > 0,\\ r \\in \\mathbb{R}","\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>>\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">u > 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\">u\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>r\u003C\u002Fmi>\u003Cmo>∈\u003C\u002Fmo>\u003Cmi mathvariant=\"double-struck\">R\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">r \\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\" style=\"margin-right:0.0278em;\">r\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-power-rule","\\log_a \\left(u^r\\right) = r \\cdot \\log_a u","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmrow>\u003Cmi>log\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cmi>a\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmrow>\u003Cmo fence=\"true\">(\u003C\u002Fmo>\u003Cmsup>\u003Cmi>u\u003C\u002Fmi>\u003Cmi>r\u003C\u002Fmi>\u003C\u002Fmsup>\u003Cmo fence=\"true\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cmo>=\u003C\u002Fmo>\u003Cmi>r\u003C\u002Fmi>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmsub>\u003Cmrow>\u003Cmi>log\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cmi>a\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmi>u\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\log_a \\left(u^r\\right) = r \\cdot \\log_a u\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:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan 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