Answer
...we apply log() or ln() to both sides,
after which we apply The Power Rule,
and we continue solving an equation which is not exponential any more.
(see details in "step by step")
Work Step by Step
An exponential equation has the unknown in one or several exponents.
If both sides can not be written as $b^{M}=b^{N},$
where M and N are expressions in x,
we apply log() or ln() to both sides (the reason is that we have these functions on our calculators),
and use The Power Rule: $\log_{\mathrm{b}}\mathrm{M}^{\mathrm{p}}=\mathrm{p}\log_{\mathrm{b}}\mathrm{M}$
by which x will no longer be in the exponent...
For example,
$ 3^{x}=140\qquad$
... apply $\log$( ) to both sides, use the Power Rule...
$\log 3^{x}=\log 140$
$x\cdot\log 3=\log 140\qquad.../\div\log 3$
... this is not exponential any more, x is not in the exponent....
$x=\displaystyle \frac{\log 140}{\log 3}$
$\log 140$ and $\log 3$ can be calculated with a calculator, so
$ x\displaystyle \approx\frac{2.14612803568}{0.47712125472}\approx$4.49807677702
