Answer
$x = \frac{e^{3}+9}{4}$
Work Step by Step
$\ln (4x - 9 )= 3$
$4x - 9 = e^{3}$
$4x = e^{3} + 9$
$x = \frac{e^{3}+9}{4}$
Check:
$\ln (4(\frac{e^{3}+9}{4}) - 9 )\overset{?}{=} 3$
$\ln (e^{3}+9 - 9 )\overset{?}{=} 3$
$\ln_{e} (e^{3})\overset{?}{=} 3$
$3= 3$
