Answer
$x=2-e$
Work Step by Step
Recall:
$$\ln{a}=y \longrightarrow e^y=a$$
Use the definition above to obtain:
\begin{align*}
\ln{(2-x)}&=1\\
e^1&=2-x\\
e&=2-x
\end{align*}
Subtract $2$ to both sides to obtain:
\begin{align*}
e-2&=2-x-2\\
e-2&=-x
\end{align*}
Multiply $-1$ to both sides of the equation to obtain:
\begin{align*}
-1(e-2)&=-x(-1)\\
-e+2&=x\\
2-e&=x
\end{align*}
