Answer
$x \approx 4.1297$
Work Step by Step
$\ln (3x-5) = 2$
$\log_e (3x-5) = 2$
$e^{2} = 3x - 5$
$e^{2} + 5 = 3x$
$x = \frac{e^{2}+5}{3}$
$x \approx 4.1297$
Check:
$\ln_e (3(\frac{e^{2}+5}{3})-5) \overset{?}{=} 2$
$\ln_e (e^{2}+5-5) \overset{?}{=} 2$
$\ln_e (e^{2}) \overset{?}{=} 2$
$2 = 2$
