## College Algebra (6th Edition)

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