Question

Выразите log√3(корень 6 степени из 1.8) через а, если log0.2(27)=a ПОМОГИТЕ!!!!!!

Answer 1

1)
$log_{0.2}27=a \ \ log{ frac{1}{5} }(3^3)=a \ \ 3log_{5^{-1}}3=a \ \ -3log_{5}3=a \ \ log_{5}3=- frac{a}{3}$

2)
$log_{ sqrt{3} } sqrt[6]{1.8}=log_{3^{ frac{1}{2} }}(1.8^{ frac{1}{6} })= frac{ frac{1}{6} }{ frac{1}{2} }log_{3}1.8= frac{1}{3}log_{3}(3*0.6)= \ \ = frac{1}{3}(log_{3}3+log_{3}0.6)= frac{1}{3}(1+log_{3}0.6)= \ \ = frac{1}{3}(1+log_{3}( frac{3}{5} ))= frac{1}{3}(1+log_{3}3-log_{3}5)= \ \ = frac{1}{3}(1+1- frac{1}{log_{5}3} )= frac{1}{3}(2- frac{1}{log_{5}3} )= \ \ = frac{2}{3}- frac{1}{3log_{5}3}= frac{2}{3}- frac{1}{3*(- frac{a}{3} )}=$
$= frac{2}{3}+ frac{1}{a}= frac{2a+3}{3a}$