Answer
$50$
Work Step by Step
\begin{align*}
\log{x}+2&=\log{2x^2} &\text{Add 2 to both sides .}\\\\
2&=\log{2x^2}-\log{x} &\text{Subtract $\log{x}$ from each side.}\\\\
2&=\log{\left(\frac{2x^2}{x}\right)} &\text{Apply the Quotient Property of Logarithms.}\\\\
2&=\log{2x}\\\\
10^2&=2x &\text{Write the equation in exponential form.}\\\\
100&=2x\\\\
50&=x &\text{Divide 2 to both sides.}\\\\
\end{align*}
