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

1 Answer
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^{-9x}=ln 16^{x-2}

-9x ln(13)=(x-2)ln16

-9x * 2.56 = (x-2) * 2.77

-23.08x = 2.77x - 5.54

-25.85x = -5.54

x = 0.214 (approx when using 2 decimal places)