# How do you solve 5=6^(3t-1) ?

Aug 2, 2016

$t = \frac{1}{3} \left(\frac{\log 5}{\log 6} + 1\right)$

#### Explanation:

Taking logs of both sides, we have:

$\log 5 = \log \left({6}^{3 t - 1}\right) = \left(3 t - 1\right) \log 6$

Divide both ends by $\log 6$ and transpose to get:

$3 t - 1 = \frac{\log 5}{\log 6}$

Add $1$ to both sides to get:

$3 t = \frac{\log 5}{\log 6} + 1$

Divide both sides by $3$ to get:

$t = \frac{1}{3} \left(\frac{\log 5}{\log 6} + 1\right)$