Answer
$x\approx2.79$
Work Step by Step
Find the natural log of both sides and then pull out the exponents on both sides. Then solve for $x$.
$5^{2x+3}=3^{x-1}$
$(2x+3)\ln(5)=(x-1)\ln(3)$
$\frac{2x+3}{x-1}=\frac{\ln(3)}{\ln(5)}$
$\frac{2x+3}{x-1}=0.68$
$0.68(x-1)=2x+3$
$0.68x-0.68=2x+3$
$0.68x=2x+3.68$
$1.32x=3.68$
$x\approx2.79$
