Question

$1) \frac{lg4}{lg64-lg8}$
$2) log_{ \frac{8}{27} } \frac{81}{16}$
$3) 5^{-6 log_{5}2}$

Answer 1

$1)\frac{lg4}{lg64-lg8}=\frac{lg4}{lg\frac{64}8}=\frac{lg4}{lg8}=log_84=log_{2^3}2^2=\frac{2}3\\\\2)log_\frac{8}{27}\frac{81}{16}=-log_\frac{8}{27}\frac{16}{81}=-log_{(\frac{2}3)^3}(\frac{2}3)^4=-\frac{4}3\\\\3)5^{-6log_52}=\frac{1}{5^{log_52^6}}=\frac{1}{2^{6log_55}}=\frac{1}{2^6}=\frac{1}{64}$