Answer
$x\approx0.08$
Work Step by Step
Find the natural log of both sides and then pull out the exponents on both sides. Then solve for $x$.
$7^{2x+1}=3^{x+2}$
$(2x+1)\ln(7)=(x+2)\ln(3)$
$\frac{2x+1}{x+2}=\frac{\ln(3)}{\ln(7)}$
$\frac{2x+1}{x+2}=0.56$
$0.56(x+2)=2x+1$
$0.56x+1.12=2x+1$
$1.12=1.44x+1$
$0.12=1.44x$
$x\approx0.08$
