# How do you solve 13^ { - 9x } = 16^ { x - 2}?

Nov 27, 2017

$x = 0.214$

#### Explanation:

Take the log of both sides and solve as you would a normal equation.

13^{-9x = ${16}^{x - 2}$

ln ${13}^{- 9 x}$=ln ${16}^{x - 2}$

$- 9 x$ ln$\left(13\right) = \left(x - 2\right)$ln16

$- 9 x \cdot 2.56 = \left(x - 2\right) \cdot 2.77$

$- 23.08 x = 2.77 x - 5.54$

$- 25.85 x = - 5.54$

$x = 0.214$ (approx when using 2 decimal places)