Question

Log2 log3 log1/3 1/27, log5 log3 3, log1/9 3√3/3, решить

Answer 1

$1)\; \; log_2log_3log_{\frac{1}{3}}\, \frac{1}{27}=log_2log_3(-log_3\, 3^{-3})=log_2log_3(log_33^3)=\\\\=log_2log_33=log_21=0\\\\2)\; \; log_5log_33=log_51=0\\\\3)log_{\frac{1}{9}}\, \frac{3\sqrt3}{3}=log_{3^{-2}}3^{\frac{1}{2}}=-\frac{1}{2}\cdot \frac{1}{2}log_33=-\frac{1}{2}\cdot \frac{1}{2}=-\frac{1}{4}$