## College Algebra (11th Edition)

$x=10^{\frac{D-200}{100}}$
$\bf{\text{Solution Outline:}}$ 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}