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)