Answer
$x=10^{\frac{D-200}{100}}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given equation, $
D=200+100\log x
,$ for $
x
,$ use the properties of equality to isolate the $\log$ expression. Then change to exponential form.
$\bf{\text{Solution Details:}}$
Using the properties of equality to isolate the $\log$ expression, the equation above is equivalent to
\begin{array}{l}\require{cancel}
D-200=100\log x
\\\\
\dfrac{D-200}{100}=\log x
.\end{array}
Since $\log_by=x$ is equivalent to $y=b^x$, the equation above, in exponential form, is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{D-200}{100}=\log_{10} x
\\\\
10^{\frac{D-200}{100}}=x
\\\\
x=10^{\frac{D-200}{100}}
.\end{array}
