Answer
$x \approx 1.771$
Work Step by Step
We wish to substitute $t=3^{x}$, so the equation becomes:
$a -(14)(\dfrac{1}{t}) -5=0 \implies a^{2}-5t-14=0 $
This gives a quadratic equation, whose factors are: $(t-7)(t+2)=0$
Use the zero factor property to obtain:
$ t-7 =0 \implies t=7$
and
$t+2=0 \implies t=-2$
But $t=3^{x}=-2$ cannot be a solution as $3^{x}$ can never be negative. So, we will consider $t=3^{x}=5$
Therefore, $3^{x}=7$
or, $x= \log_3 7 \approx 1.771$
Thus, our answer is: $x \approx 1.771$
