Answer
$x \approx12.3995$
Work Step by Step
$\ln (4x+5) = 4$
$\log_e (4x+5) = 4$
$4x + 5 = e^{4}$
$4x = e^{4} - 5$
$x = \frac{e^{4}-5}{4}$
$x \approx12.3995$
Check:
$\ln (4( \frac{e^{4}-5}{4})+5) \overset{?}{=} 4$
$\ln(e^{4}-5+5) \overset{?}{=} 4$
$\log_e (e^{4}) \overset{?}{=} 4$
$4 = 4$