well, if you recall that a logarithm is just another notational way to express an exponential, then [tex]\bf log_{{ a}}{{ b}}=y \iff {{ a}}^y={{ b}}\qquad\qquad
{{ a}}^y={{ b}}\iff log_{{ a}}{{ b}}=y \\\\
-----------------------------\\\\
thus\qquad log_3(x^6)=12 \iff 3^{12}=x^6[/tex]
[tex]\bf -----------------------------\\\\
thus\qquad log_3(x^6)=12 \iff 3^{12}=x^6\impliedby taking\ \sqrt[6]{\qquad }
\\\\\\
\sqrt[6]{3^{12}}=\sqrt[6]{x^6}\implies \sqrt[6]{3^{12}}=x
\\\\\\
\textit{now, recall }3^{12}\implies 3^{2\cdot 6}\implies (3^2)^6\qquad thus
\\\\\\
\sqrt[6]{(3^2)^6}=x\implies 3^2=x\implies 9=x[/tex]
