Answer
$t = \frac{1}{4.3e^{4.5}}$
Work Step by Step
$\ln (4.3t) + 7.5 = 3$
$\ln 4.3t = -4.5$
$4.3t = e^{-4.5}$
$4.3t = \frac{1}{e^{4.5}}$
$t = \frac{1}{e^{4.5}}(\frac{1}{4.3})$
$t = \frac{1}{4.3e^{4.5}}$
Check:
$\ln (4.3t) + 7.5 \overset{?}{=} 3$
$\ln (4.3(\frac{1}{4.3e^{4.5}})) + 7.5 \overset{?}{=} 3$
$\ln (\frac{1}{e^{4.5}}) + 7.5 \overset{?}{=} 3$
$\ln (e^{-4.5}) \overset{?}{=} -4.5$
$-4.5 = -4.5$
