Question

calcule 81 elevado a log de 2 base 3

Answer 1

$81^{\log_32}=k\\\\\log_{81}k=\log_32\Rightarrow\log_ab=x\Leftrightarrow\,a^x=b\\\\\log_{3^4}k=\log_32\\\\\frac{1}{4}\cdot\log_3k=\log_32$

$\log_3k^{\frac{1}{4}}=\log_32\\\\k^{\frac{1}{4}}=2\\\\\sqrt[4]{k}=2\\\\k=2^4\\\\\boxed{k=16}$