Chapter 6 - Logarithmic Functions - 6.6 Solving Logarithmic Equations - 6.6 Exercises - Page 535: 37

$t \approx 0.045$

$\ln (3t) + 5 =3$ $\ln 3t = 3 -5$ $\ln 3t = -2$ $\log_e 3t = -2$ $e^{-2} = 3t$ $t = \frac{e^{-2}}{3}$ $t \approx 0.045$ Check: $\ln (3(\frac{e^{-2}}{3})) + 5 \overset{?}{=}3$ $\ln (e^{-2}) + 5 \overset{?}{=}3$ $\ln(e^{-2}) + 5 \overset{?}{=}3$ $(-2)\log_e(e) + 5 \overset{?}{=}3$ $-2 + 5 \overset{?}{=}3$ $3 = 3$