Answer
$x \approx 0.466$
Work Step by Step
$3(5^{3x+2})-700=11$
$3(5^{3x+2})=11+700$
$3(5^{3x+2})=711$
$(5^{3x+2})=\frac{711}{3}$
$(5^{3x+2})=237$
$\log5^{3x+2}= \log237$
$(3x+2)\log5=\log237$
$3x+2=\frac{\log237}{\log5}$
$3x+2=3.397$
$3x=3.397-2$
$3x=1.397$
$x=\frac{1.397}{3}$
$x \approx 0.466$
