Question

упростить выражение log1/3 54 - 1/3log1/3 8+log1/3 81

Answer 1

Объяснение:

$log_{ \frac{1}{3} }(54) - \frac{1}{3} log_{ \frac{1}{3} }(8) + log_{ \frac{1}{3} }(81) = log_{ \frac{1}{3} }(54) - log_{ \frac{1}{3} }( {8}^{ \frac{1}{3} } ) + log_{ \frac{1}{3} }(81) = log_{ \frac{1}{3} }(54) - log_{ \frac{1}{3} }(2) + log_{ \frac{1}{3} }(81) = log_{ \frac{1}{3} }( \frac{54}{2} \times 81 ) = log_{ \frac{1}{3} }( {3}^{3} \times {3}^{4} ) = log_{ \frac{1}{3} }( {3}^{7} ) = -7 log_{ 3 }(3)$