Chapter 6 - Logarithmic Functions - 6.6 Solving Logarithmic Equations - 6.6 Exercises - Page 535: 66

$x = \frac{1}{e^{2}}$

$\ln x + 7 = 5$ $\ln x = 5 - 7$ $\ln x = -2$ $x = e^{-2}$ $x = \frac{1}{e^{2}}$ Check: $\ln x + 7 \overset{?}{=} 5$ $\ln e^{-2} + 7 \overset{?}{=} 5$ $-2\ln e + 7 \overset{?}{=} 5$ $-2(1) + 7 \overset{?}{=} 5$ $-2 + 7 \overset{?}{=} 5$ $5 = 5$