Answer
Yes, please see explanation in the step-by-step section.
Work Step by Step
For $x\gt 0$ and $a$, a positive constant other than 1,
$\log_{a}x$ is the exponent to which $a$ must be raised in order to get $x$.
Thus, $\log_{a}x=m$ means $a^{m}=x$
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By definition, $\log_{b} a=x$ means that $b^{x}=a.$
Then, applying $(x^{m})^{n}=x^{mn}$, it follows that
$b=a^{1/x}$
that is,
the exponent by which we raise a to obtain b is $1/x.$
This is written as
$\log_{a}b=1/x$
