Answer
No solutions.
Work Step by Step
We have to solve the exponential equation:
$3^{4x+3}=81^{x}$
Rewriting $81$ as $3^{4}$, we have
$3^{4x+3}=(3^{4})^{x}$
$\implies 3^{4x+3}=3^{4x}$
Equating the exponents, we have
$4x+3=4x$ or $4x-4x+3=0$
$\implies 3=0$ which is never true.
So, the above equation has no solutions.
