Question

log de 64 com base 8 - log de 0,001 com base 10 é igual a

Answer 1

Para facilitar, vamos calcular os dois logaritmos separadamente e, posteriormente, podemos determinar o valor da expressão.

$log_{_8}64~=~x\\\\\\Aplicando~a~de finicao~de~logaritmo:\\\\\\64~=~8^x\\\\\\8^2~=~8^x\\\\\\\backslash\!\!\!8^2~=~\backslash\!\!\!8^x\\\\\\\boxed{ x~=~2}\\\\\\\\\log0,001~=~y\\\\\\Aplicando~a~de finicao~de~logaritmo:\\\\\\0,001~=~10^y\\\\\\10^{-3}~=~10^y\\\\\\\backslash\!\!\!\!10^{-3}~=~\backslash\!\!\!\!10^y\\\\\\\boxed{y~=\,-3}$

Montando e resolvendo a expressão dada no enunciado, temos:

$\log_{_8}64~-~\log0,001~=\\\\\\=~x~-~y\\\\\\=~2~-~(-3)\\\\\\=~2+3\\\\\\=~\boxed{~5~}~~\Rightarrow~Resposta\\\\\\\Huge{\begin{array}{c}\Delta \tt{\!\!\!\!\!\!\,\,o}\!\!\!\!\!\!\!\!\:\,\perp\end{array}}Qualquer~d\acute{u}vida,~deixe~ um~coment\acute{a}rio$