## College Algebra (11th Edition)

$x=2-10^{0.5}$
$\bf{\text{Solution Outline:}}$ To solve the given equation, $\log(2-x)=0.5 ,$ convert to exponential form. Then use the properties of equality to isolate the variable. $\bf{\text{Solution Details:}}$ Since $\log x=\log_{10} x,$ the equation above is equivalent to \begin{array}{l}\require{cancel} \log_{10}(2-x)=0.5 .\end{array} Since $y=b^x$ is equivalent to $\log_b y=x,$ the exponential form of the equation above is \begin{array}{l}\require{cancel} 10^{0.5}=2-x .\end{array} Using the properties of equality, the equation above is equivalent to \begin{array}{l}\require{cancel} x=2-10^{0.5} .\end{array}