Question

Решить логарифмы прикреплённые на фото

Answer 1

Ответ:

1.

$log_{6}(216) \times log_{9}(729) = log_{6}( {6}^{3} ) \times log_{9}( {9}^{3} ) = 3 \times 3 = 9$

2.

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

3.

${9}^{ log_{3}(7) } = {3}^{2 log_{3}(7) } = {3}^{ log_{3}( {7}^{2} ) } = {7}^{2} = 49$

4.

$log_{0.2}(125) = log_{ \frac{1}{5} }( {5}^{3} ) = log_{ {5}^{ - 1} }( {5}^{3} ) = - 1 \times 3 log_{5}(5) = - 3$

5.

$log_{25}(0.2) = log_{ {5}^{2} }( \frac{1}{5} ) = \frac{1}{2} \times ( - 1) log_{5}(5) = - 0.5$