Answer
$c = \frac{e^{5} + 7}{2}$
Work Step by Step
$\ln(2c - 7) = 5$
$\log_e (2c - 7) = 5$
$e^{5} = 2c - 7$
$e^{5} + 7 = 2c$
$c = \frac{e^{5} + 7}{2}$
Check:
$\ln(2(\frac{e^{5} + 7}{2}) - 7) \overset{?}{=} 5$
$\ln (e^{5} + 7 - 7) \overset{?}{=} 5$
$\ln(e^{5} ) \overset{?}{=} 5$
$5 \log_e e \overset{?}{=} 5$
$5(1) \overset{?}{=} 5$
$5 = 5$
