Question

Вычислите
$2 log_{30}5 - \frac{1}{3} log_{30}125 + 0.5 log_{30}36$

Answer 1

$2log_{30}5-\frac{1}{3}log_{30}125+0.5log_{30}36=\\log_{30}5^2-log_{30}125^{\frac{1}{3}}+log_{30}36^{0.5}=\\log_{30}25-log_{30}5+log_{30}6=\\log_{30}(\frac{25}{5}\cdot6)=log_{30}30=1$