Answer
$x=\frac{\log 3+\log 5}{4\log 3-2\log 5}\approx 2.303600$
Work Step by Step
We solve for $x$:
$5^{2x+1} =3^{4x-1}$
$(2x+1)\log 5=(4x-1)\log 3$
$2x\log 5+\log 5=4x\log 3-\log 3$
$2x\log 5-4x\log3=-\log 3-\log 5$
$x(2 \log 5-4\log 3)=-\log 3-\log 5$
$x=\frac{\log 3+\log 5}{4\log 3-2\log 5}\approx 2.303600$
