Answer
$x=-2$
Work Step by Step
The given equation is
$\Rightarrow 7^{3x+5}=7^{x+1}$
Equate the exponents.
$\Rightarrow 3x+5=x+1$
Add $-x-5$ to each side.
$\Rightarrow 3x+5-x-5=x+1-x-5$
Simplify.
$\Rightarrow 2x=-4$
Divide each side by $2$.
$\Rightarrow \frac{2x}{2}=\frac{-4}{2}$
Simplify.
$\Rightarrow x=-2$
Check $x=-2$.
$\Rightarrow 7^{3(-2)+5}=7^{-2+1}$
$\Rightarrow 7^{-6+5}=7^{-1}$
$\Rightarrow 7^{-1}=7^{-1}$
True.
