Question

Помогите вычислить логарифм.

Answer 1

$frac{log_32+log_3(3log_{frac{1}{3}}tgfrac{pi}{6})}{log_{pi }5cdot log_3pi } =frac{log_32+log_3(-3log_3frac{1}{sqrt3})}{frac{log_{pi }5}{log_{pi }3}} =frac{log_32+log_3(-3log_3(3^{-frac{1}{2}}))}{log_35}=\\= frac{log_32+log_3(frac{3}{2})}{log_35} = frac{log_32+(log_33-log_32)}{log_35} = frac{log_32+1-log_32}{log_35}= frac{1}{log_35} =log_53$