Intermediate Algebra for College Students (7th Edition)

$x=\frac{1}{2}$
First, we let $\log_{6}{\sqrt6} = x$ RECALL: $\log_b{y} =x \longrightarrow b^x=y$ Use the rule above, where $y=\sqrt6$ and $b=6$, to obtain: $6^x=\sqrt6$ Write $\sqrt6$ as $6^{\frac{1}{2}}$ to obtain: $6^x=6^{\frac{1}{2}}$ Use the rule "If $a^x=a^y$, then $x=y$" to obtain: $x=\frac{1}{2}$