[tex]\bf \textit{logarithm of factors}
\\\\
log_a(xy)\implies log_a(x)+log_a(y)\\\\
-------------------------------\\\\
log_3(27\sqrt[3]{3})\qquad
\begin{cases}
27=3\cdot 3\cdot 3\\
\qquad 3^3\\
\sqrt[3]{3}=\sqrt[3]{3^1}\\
\qquad 3^{\frac{1}{3}}
\end{cases}\implies log_3\left( 3^3\cdot 3^{\frac{1}{3}} \right)
\\\\\\
log_3\left( 3^{3+\frac{1}{3}} \right)\implies log_3\left( 3^{\frac{4}{3}} \right)\implies \cfrac{4}{3}\cdot log_3(3)\implies \cfrac{4}{3}\cdot 1\implies \cfrac{4}{3}[/tex]
