Question

How do you this? log(3)x^6=12

Answer 1

Well, if you recall that a logarithm is just another notational way to express an exponential, then $\bf log_{{ a}}{{ b}}=y \iff {{ a}}^y={{ b}}\qquad\qquad {{ a}}^y={{ b}}\iff log_{{ a}}{{ b}}=y \\\\ -----------------------------\\\\ thus\qquad log_3(x^6)=12 \iff 3^{12}=x^6$

$\bf -----------------------------\\\\ thus\qquad log_3(x^6)=12 \iff 3^{12}=x^6\impliedby taking\ \sqrt[6]{\qquad } \\\\\\ \sqrt[6]{3^{12}}=\sqrt[6]{x^6}\implies \sqrt[6]{3^{12}}=x \\\\\\ \textit{now, recall }3^{12}\implies 3^{2\cdot 6}\implies (3^2)^6\qquad thus \\\\\\ \sqrt[6]{(3^2)^6}=x\implies 3^2=x\implies 9=x$