Question

Помогите с логарифмами

Answer 1

$log_{sqrt2}4=log_{2^{1/2}}2^2=2cdot 2=4\\log_{sqrt3}81=log_{3^{1/2}}3^4=4cdot 2=8\\log_{0,5}sqrt[3]2=log_{2^{-1}}2^{1/3}=-frac{1}{3}\\log_{0,25}sqrt[3]4=log_{4^{-1}}4^{frac{1}{3}=-frac{1}{3}}\\log_{frac{1}{3}}9=log_{3^{-1}}3^2=-2\\log_{2sqrt2}; frac{1}{8}=log_{2^frac{5}{2}}2^{-3}=-frac{6}{5}=-1,2$