Chapter 6 - Logarithmic Functions - 6.6 Solving Logarithmic Equations - 6.6 Exercises - Page 535: 38

$t \approx 0.001$

$\ln (2t) + 8 = 2$ $\ln(2t) + 8 = 2$ $\ln (2t) = 2-8$ $\log_e (2t) = -6$ $e^{-6} = 2t$ $t = \frac{e^{-6}}{2}$ $t \approx 0.001$ Check: $\ln (2(\frac{e^{-6}}{2})) + 8 \overset{?}{=} 2$ $\ln(e^{-6}) + 8 \overset{?}{=} 2$ $-6\log_e (e) + 8 \overset{?}{=} 2$ $-6(1) + 8 \overset{?}{=} 2$ $-6 + 8 \overset{?}{=} 2$ $2 = 2$