Question

Qual o valor numérico de:

$log_{1/3} ( 4^{ log_{2} 9} )$

Answer 1

$log_{ \frac{1}{3} }\left(4^{log_2(9)\right)\\\\= log_2(9)*log_{ \frac{1}{3}} (4)\\\\log_2(3^2)*log_{ \frac{1}{3}} (2^2)\\\\=2*log_2(3)*2*-(log_{3}(2))}\\\\=-4*log_2(3)*log_3(2)\\\\-4* \frac{log(3)}{log(2)}* \frac{log(2)}{log(3)} \\\\=-4$