Question

log(осн.1/4)(log(осн.3)4*log(осн.2)3)=...

Answer 1

$log(1/4)[log(3)4*log(2)3]=log(1/4)[2/log(2)3*log(2)3]=log(1/4)2=$$-1/2$

Answer 2

$log_{ \frac{1}{4} } ( log_{3} 4*log_{2} 3)=log_{2^{-2} } ( \frac{log_{2} 4}{log_{2} 3} * \frac{log_{2} 3}{log_{2} 2})= \\ = - \frac{1}{2} log_{2} ( \frac{log_{2} 4*log_{2} 3}{log_{2} 3*log_{2} 2})= \\ =- \frac{1}{2} log_{2}( \frac{2}{1} ) = - \frac{1}{2} log_{2}2 = - \frac{1}{2} = - 0,5$