# How do you solve 13^(3x)-1=91?

Aug 8, 2018

The solution is $= 0.59$

#### Explanation:

The equation is

${13}^{3 x} - 1 = 91$

$\implies$, ${13}^{3 x} = 91 + 1 = 92$

Taking logs on both sides

$\ln \left({13}^{3 x}\right) = \ln \left(92\right)$

$3 x \ln \left(13\right) = \ln \left(92\right)$

$x = \frac{\ln 92}{3 \cdot \ln 13} = 0.59$