Question

вычислите значение выражения log1/4(2√2-√6)+log1/4(2√2+√6)

Answer 1

$log_{1/4}(2sqrt2-sqrt6)+log_{1/4}(2sqrt2+sqrt6)=\ =log_{1/4}(2sqrt2-sqrt6)(2sqrt2+sqrt6)=log_{1/4}(8-6)=log_{1/4}2= \ =log_{2^{-2}}2=-frac{1}{2}$

Answer 2

= log1/4((2√2-√6)*(2√2+√6)) = log1/4((2√2)^2 - (√6)^2) = -1/2 log2(4*2-6) = -1/2 log2(2) = -1/2