# How do you solve 5e^(3t) = 8e^(2t)?

Jun 14, 2016

$t = {\log}_{e} \left(\frac{8}{5}\right)$

#### Explanation:

After some trasformations we get at

${e}^{3 t} / \left({e}^{2 t}\right) = \frac{8}{5}$ or ${e}^{t} = \frac{8}{5}$

Solving for $t$ we have

$t {\log}_{e} e = t \times 1 = t = {\log}_{e} \left(\frac{8}{5}\right)$