Solve the exponential equation. 27^4x=9 how?

1 Answer
May 20, 2018

#x=1/6#

Explanation:

#27^(4x) =9#

First notice that #27=3^3 and 9=3^2#

In solving exponential equations first look to see if you can express both sides to the same base. In this case you can.

#(3^3)^(4x) = 3^2#

#3^(12x) = 3^2#

We can now apply a law of exponents: If #a^x=a^y# then #x=y#

Hence, #12x=2 -> x=1/6#

NB: If you can't find a way to reduce both sides to the same base, then try taking logs of both sides:

#4xln27 = ln9#

#4x = ln9/ln27 approx 2.19722/3.29584 approx 0.66666#

#:. x approx 0.66666/4 approx 0.16667#