Question

O valor de log9(log8 2)

Answer 1

Resposta:2

Explicação passo a passo:

Log(9) 8 = Log 8/Log 9

2Log(8) 9 = 2Log 9/Log 8

Então: Log 8/Log 9 . 2Log9/Log8 = 2

Espero ter ajudado ♡♡♡♡♡

Bons estudos!

Answer 2

Calcular primeiro log₈2:

$\sf \log_82~=~x\\\\\\2~=~8^x\\\\\\2~=~\left(2^3\right)^x\\\\\\2^1~=~2^{3x}\\\\\\2^1~=~2^{3x}\\\\\\1~=~3x\\\\\\x~=~\dfrac{1}{3}$

Calcular o valor da expressão:

$\sf \log_9(\log_82)~=~y\\\\\\\log_9(x)~=~y\\\\\\\log_9\left(\dfrac{1}{3}\right)~=~y\\\\\\\dfrac{1}{3}~=~9^y\\\\\\3^{-1}~=~\left(3^2\right)^y\\\\\\3^{-1}~=~3^{2y}\\\\\\-1~=~2y\\\\\\y~=\,-\dfrac{1}{2}$