Answer
$t = -16.2$
Work Step by Step
$\log_3 (-5t) + 13 = 17$
$\log_3 (-5t) = 17 - 13$
$\log_3 (-5t) = 4$
$3^{4} = -5t$
$81 = -5t$
$t = -\frac{81}{5}$
$t = -16.2$
Check:
$\log_3 (-5(-16.2)) + 13 \overset{?}{=} 17$
$\log_3 (81) + 13 \overset{?}{=} 17$
$\log_3 (3^{4}) + 13 \overset{?}{=} 17$
$4\log_3 (3) + 13 \overset{?}{=} 17$
$4(1) + 13 \overset{?}{=} 17$
$4+ 13 \overset{?}{=} 17$
$17 = 17$
