Answer
$y=15$
Work Step by Step
Using the properties of logarithms, the given equation, $
\log(7y-5)=2
,$ is equivalent to
\begin{align*}\require{cancel}
\log_{10}(7y-5)&=2
\\
7y-5&=10^2
&\left(b^x=y\text{ implies }\log_by=x \right)
\\
7y-5&=100
\\
7y-5+5&=100+5
\\
7y&=105
\\\\
\dfrac{7y}{7}&=\dfrac{105}{7}
\\\\
y&=15
.\end{align*}
Hence, the solution is $
y=15
.$
