Question

Simplificando a expressão log3 2.log4 9.Log8 27.log27 4,obtém-se
Resposta
A)1/2
B)1/3
C)1/4
D)2/3
E)2/5

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\mathsf{log_3\:2 \times log_4\:9 \times log_8\:27 \times log_{27}\:4}$

$\mathsf{log_3\:2 \times log_{2^2}\:3^2 \times log_{2^3}\:3^3\times log_{3^3}\:2^2}$

$\mathsf{log_3\:2 \times log_{2}\:3 \times log_{2^3}\:3^3\times log_{3^3}\:2^2}$

$\mathsf{1 \times log_{2^3}\:3^3\times log_{3^3}\:2^2}$

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

$\mathsf{1 \times \dfrac{2}{3} \times 1}$

$\boxed{\boxed{\mathsf{log_3\:2 \times log_4\:9 \times log_8\:27 \times log_{27}\:4 = \dfrac{2}{3}}}}\leftarrow\textsf{letra D}$