Answer
The value of x is 3.5850.
Work Step by Step
Consider the exponential equation.
${{2}^{x}}=12$
$x={{\log }_{2}}12$
Use the base change formula and solve.
$x=\frac{\log 12}{\log 2}$
Use a calculator and solve.
$\begin{align}
& x\approx \frac{1.079}{0.3010} \\
& =3.5847
\end{align}$
Check:
Substitute $x=3.5847$ in the given equation.
$\begin{matrix}
{{2}^{3.5847}}\overset{?}{\mathop{=}}\,12 \\
\text{ }11.99\overset{?}{\mathop{=}}\,12 \\
\text{ }12\approx 12 \\
\end{matrix}$
Thus, the obtained solution is correct.
