Question

Determine o valor da expressao log 2 64 + log 3 9 - log 5 125

Answer 1

Obs.: Quando respondi a questão, o editor de formulas estava com problemas. Caso os calculos estejam desformatados, considere a figura anexada.

Vamos calcular os logaritmos individualmente para daí então determinarmos o valor da expressão.

$log_{_2}64~=~x\\\\\\64~=~2^x\\\\\\2^6~=~2^x\\\\\\\boxed{x~=~6}\\\\\\\\log_{_3}9~=~y\\\\\\9~=~3^y\\\\\\3^2~=~3^y\\\\\\\boxed{y~=~2}\\\\\\\\log_{_5}125~=~z\\\\\\125~=~5^z\\\\\\5^3~=~5^z\\\\\\\boxed{z~=~3}$

Agora, calculando a expressão, temos:

$log_{_2}64~+~log_{_3}9~-~log_{_5}125\\\\\\x~+~y~-~z\\\\\\6~+~2~-~3\\\\\\\boxed{5}$