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

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Answer 1 · 2017-11-27T19:47:56

#x=0.214#

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)