## College Algebra (11th Edition)

$x=10^{\frac{D-160}{10}}$
$\bf{\text{Solution Outline:}}$ 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}