Question

Вычислите $3^{-a^{2} * log_{2}9 }$, если $3^{a}=2$.

Answer 1

$3^{-a^2*log_29}= frac{1}{3^{a^2log_29}}= frac{1}{(3^{a})^{alog_29}}= frac{1}{2^{alog_29}}= frac{1}{2^{log_29^{a}}}= frac{1}{9^{a}}= frac{1}{3^{2a}}= frac{1}{(3^{a})^2}$
$= frac{1}{2^2}= frac{1}{4}$