Question

Log de base 3 raiz de 3 logaritimando 27, como resolver?

Answer 1

Lembrando que:

$\rightarrow~\sqrt[b]{a^c}~=~a^{\frac{c}{b}}\\\\\rightarrow~a^b~.~a^c~=~a^{\,b+c}\\\\\rightarrow~\left(a^b\right)^c~=~a^{\,b~.~c}$

$log_{_{3\sqrt{3}}}\,27~=~x\\\\\\27~=~\left(3\sqrt{3}\right)^x\\\\\\3^3~=~\left(3^{\,1+\frac{1}{2}}\right)^x\\\\\\3^3~=~\left(3^{\frac{3}{2}}\right)^x\\\\\\3^3~=~3^{\,\frac{3}{2}~.~x}\\\\\\3~=~\frac{3}{2}x\\\\\\x~=~3~.~\frac{2}{3}\\\\\\x~=~\frac{6}{3}\\\\\\\boxed{x~=~2}$