Question

Полное решение логорифмов.

Answer 1

1.

  $log_2(log_4(log_864))=log_2(log_4(log_88^2))=log_2(log_4(2log_88))=log_2(log_42)=$

= $log_2(log_44^{1/2})=log_2(\frac{1}{2} log_44)=log_2(\frac{1}{2})=log_2(2^{-1})}=-1log_22=-1$

Ответ:  -1

2.

$log_248+log_2\frac{5}{3} +log_2\frac{4}{5}=log_2(48*\frac{5}{3}*\frac{4}{5} )=log_264=log_22^6=6log_22=6$

Ответ:  6

3.

$1)log_{\sqrt{27} }3}=log_{\sqrt{27}}(\sqrt{27})^{2/3} =\frac{2}{3} log_{\sqrt{27}}(\sqrt{27})}=\frac{2}{3}$

$2)log_{\sqrt{3} }3}=log_{\sqrt{3}}(\sqrt{3})^{2} =2 log_{\sqrt{3}}(\sqrt{3})}=2$

$\frac{1}{log^2_{\sqrt{27} }3}- \frac{1}{log^2_{\sqrt{3}}3}=\frac{1}{(2/3)^2}-\frac{1}{2^2}=\frac{9}{4}-\frac{1}{4}=\frac{8}{4}=2$

Ответ: 2