Answer
$t \approx 6.325$
Work Step by Step
$\log (5t^{3}) - \log (2t) = 2$
$\log \frac{5t^{3}}{2t} = 2$
$\log \frac{5t^{2}}{2} = 2$
$10^{2} = \frac{5t^{2}}{2}$
$100 = \frac{5t^{2}}{2}$
$200 = 5t^{2}$
$t^{2} = 40$
$t = ±\sqrt {40}$
$t \approx 6.325$
Since we can't take the log of a negative number, the only possible solution is $t = \sqrt {40}$. $t \approx 6.325$.
Check:
$\log (5(\sqrt {40})^{3}) - \log (2(\sqrt {40})) \overset{?}{=} 2$
$\log (5(252.982...) - \log (12.6491...) \overset{?}{=} 2$
$\log (1264.911...) - \log (12.6491...) \overset{?}{=} 2$
$\log \frac{(1264.911...)}{(12.6491...)} \overset{?}{=} 2$
$\log 100 \overset{?}{=} 2$
$ 2 = 2$
