#### Answer

$x=2-10^{0.5}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
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}