Question

Помогите решить примеры

Answer 1

Ответ:

$1) log_{3}( {3}^{2} ) = 2 \\ 2) log_{ {5}^{ - 1} }( {5}^{2} ) = - 1 \times 2 \times log_{5}(5) = - 2 \\ 3) log_{3}( {3}^{ - 1} ) = - 1$

$4) log_{ \frac{1}{3} }( \frac{1}{ {3}^{2} } ) = 2$

$5) log_{3}( {3}^{4} ) = 4 \\ 6) log_{ {4}^{ - 1} }( {4}^{2} ) = - 1 \times 2 \times log_{4}(4) = - 2$

$7) log_{ {3}^{ - 1} }( {3}^{3} ) = - 1 \times 3 \times log_{3}(3) = - 3 \\ 8) log_{7}( {7}^{2} ) = 2 \\ 9)log_{ {5}^{ - 1} }( {5}^{3} ) = - 1 \times 3 \times log_{5}(5) = - 3$

$10) log_{6}( {6}^{ - 2} ) = - 2$

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$1) log_{ {3}^{3} }( {3}^{2} ) = \frac{1}{3} \times 2 \times log_{3}(3) = \frac{2}{3}$

$2) log_{ {5}^{3} }( {5}^{2} ) = \frac{1}{3} \times 2 \times log_{5}(5) = \frac{2}{3} \\ 3) log_{ {10}^{2} }(10) = \frac{1}{2}$

$4) log_{ {2}^{5} }( {2}^{6} ) = \frac{1}{5} \times 6 \times log_{2}(2) = \frac{6}{5}$

$5) log_{ {6}^{2} }( {6}^{3} ) = \frac{3}{2} \\ 6) log_{ {3}^{3} }( {3}^{4} ) = \frac{4}{3}$

$7) log_{ {9}^{2} }(9) = \frac{1}{2} \\ 8) log_{ {10}^{3} }( {10}^{2} ) = \frac{2}{3}$

$9) log_{ {7}^{3} }( {7}^{2} ) = \frac{2}{3}$

$10) log_{ {2}^{5} }( {2}^{3} ) = \frac{3}{5}$