Question

simplificando o log (log(9) 4 )* (log(16)81)*(log(27))(8*log(8)3) obtemos

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\mathsf{log_9\:4 \times log_{16}\:81 \times log_{27}\:8 \times log_8\:3}$

$\mathsf{log_{3^2}\:4 \times log_{4^2}\:3^4 \times log_{3^3}\:8 \times log_8\:3}$

$\mathsf{\dfrac{1}{2}\:log_{3}\:4 \times \dfrac{4}{2}\:log_{4}\:3 \times \dfrac{1}{3}\:log_{3}\:8 \times log_8\:3}$

$\mathsf{log_{3}\:4 \times log_{4}\:3 \times \dfrac{1}{3}\:log_{3}\:8 \times log_8\:3}$

$\boxed{\boxed{\mathsf{log_9\:4 \times log_{16}\:81 \times log_{27}\:8 \times log_8\:3 = \dfrac{1}{3}}}}$