Answer
$x=10^{\frac{D-160}{10}}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given equation, $
D=160+10\log x
,$ in terms of $
x
,$ use the properties of equality to isolate the logarithmic expression. Then change to exponential form. Finally use again the properties of equality to isolate the needed variable.
$\bf{\text{Solution Details:}}$
Using the properties of equality, the equation above is equivalent to
\begin{array}{l}\require{cancel}
D-160=10\log x
\\\\
\dfrac{D-160}{10}=\dfrac{10\log x}{10}
\\\\
\dfrac{D-160}{10}=\log x
\\\\
\log x=\dfrac{D-160}{10}
.\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}
\log_{10} x=\dfrac{D-160}{10}
\\\\
x=10^{\frac{D-160}{10}}
.\end{array}
