Question

Log[³√3]27?????????????

Answer 1

Definição de logaritmo:

Se $a~\textgreater~0$ e $b~\textgreater~0,~b\neq1$, então

$\boxed{\boxed{\log_{b}a=c~\Leftrightarrow~b^{c}=a}}$
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$\log_{\sqrt[3]{3}}\,27=x~\Leftrightarrow~(\sqrt[3]{3})^{x}=27$

Resolvendo a equação exponencial:

$(\sqrt[3]{3})^{x}=27\\\\(3^{1/3})^{x}=3^{3}\\\\3^{(1/3)\cdot x}=3^{3}\\\\3^{x/3}=3^{3}~~\Leftrightarrow~~\dfrac{x}{3}=3~~\Leftrightarrow~~x=3\cdot3=9$

Portanto,

$\boxed{\boxed{\log_{\sqrt[3]{3}}\,27=9}}$