Answer
The solution set is $\{\log_{3}7\}$ or $\{1.771\}$.
Work Step by Step
... Substitute $t=3^{x}$ (t is positive)
... the equation becomes
$t-14\displaystyle \cdot\frac{1}{t}-5=0 \quad $... multiply with t
$t^{2}-14-5t=0 \quad $... rewrite, in order of powers
$t^{2}-5t-14=0 \quad $...
... two factors of $-14$ whose sum is $-5$ ... are $-7$ and $+2$
$(t-7)(t+2)=0\quad \Rightarrow\quad t=7$ or $t=-2$
... Since t must be positive, discard the $t=-2$ solution.
... Bring back x
$t=7$
$3^{x}=7 \quad $...Apply$: \quad \log_{3}(...)$
$x=\log_{3}7\approx 1.771$
The solution set is $\{\log_{3}7\}$ or $\{1.771\}$
