Question

log₃ $frac{1}{9}$ + log₉ $frac{1}{9}$ - $frac{1}{3}$ log₂₇ $frac{1}{9}$

Answer 1

$log_3frac{1}{9}+log_9frac{1}{9}-frac{1}{3}cdot log_{27}frac{1}{9}=log_33^{-2}+log_99^{-1}-frac{1}{3}cdot log_{3^3}3^{-2}=\\=-2log_33-1cdot log_99-frac{1}{3}cdot frac{-2}{3}cdot log_33=-2-1+frac{2}{9}=-3+frac{2}{9}=-2frac{7}{9}$