Помогите решить логарифмы. Created by Tatyanka25. algebra-ru

Помогите решить логарифмы...

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$5^{1+log_5 3}=5\cdot5^{log_5 3}=5\cdot3=15, \\ 10^{1-lg 2}=\frac{10}{10^{lg2}}=\frac{10}{2}=5, \\ (\frac{1}{7})^{1+log_{\frac{1}{7}} 2}=\frac{1}{7}\cdot(\frac{1}{7})^{log_{\frac{1}{7}} 2}=\frac{1}{7}\cdot2=\frac{2}{7}, \\ 3^{2-log_3 18}=\frac{3^2}{3^{log_3 18}}=\frac{9}{18}=\frac{1}{9}; \\$

$4^{2log_2 3}=(2^2)^{2log_2 3}=2^{4log_2 3}=(2^{log_2 3})^4=3^4=81, \\ 5^{-3log_5 \frac{1}{2}}=(5^{log_5 \frac{1}{2}})^{-3}=(\frac{1}{2})^{-3}=2^3=8, \\ (\frac{1}{2})^{4log_{\frac{1}{2}} 3}=((cc)^{log_{\frac{1}{2}} 3})^4=3^4=81, \\ 6^{-2log_6 5}=(6^{log_6 5})^{-2}=5^{-2}=\frac{1}{5^2}=\frac{1}{25}; \\$

$log_3 (\sqrt[5]{a^3b})^{\frac{2}{3}}=log_3 ((a^3b)^\frac{1}{5})^\frac{2}{3}=log_3 (a^3b)^\frac{2}{15}=log_3 ((a^3)^\frac{2}{15}b^\frac{2}{15})= \\ =log_3 (a^\frac{2}{5}b^\frac{2}{15})=log_3 a^\frac{2}{5}+log_3 b^\frac{2}{15}=\frac{2}{5} log_3 a + \frac{2}{15} log_3 b; \\ log_3 (9a^4\sqrt[5]{b})=log_3 3^2 + log_3 a^4 + log_3 b^\frac{1}{5}=2+4log_3 a + \frac{1}{5}log_3 b.$

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Настюффка1999

5^{1+log_5 3}=5\cdot5^{log_5 3}=5\cdot3=15, \\ 10^{1-lg 2}=\frac{10}{10^{lg2}}=\frac{10}{2}=5, \\ (\frac{1}{7})^{1+log_{\frac{1}{7}} 2}=\frac{1}{7}\cdot(\frac{1}{7})^{log_{\frac{1}{7}} 2}=\frac{1}{7}\cdot2=\frac{2}{7}, \\ 3^{2-log_3 18}=\frac{3^2}{3^{log_3 18}}=\frac{9}{18}=\frac{1}{9};

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