SOLUTION: I am stuck on this problem. {{{(2/3)^(x-2) = (9/4)^(2x-1)}}}

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: I am stuck on this problem. {{{(2/3)^(x-2) = (9/4)^(2x-1)}}}      Log On


   

Question 340237: I am stuck on this problem.
%282%2F3%29%5E%28x-2%29+=+%289%2F4%29%5E%282x-1%29
Found 2 solutions by fractalier, jrfrunner:
Answer by fractalier(6550) About Me  (Show Source):
You can put this solution on YOUR website!
From
%282%2F3%29%5E%28x-2%29+=+%289%2F4%29%5E%282x-1%29
realize that 9/4 is (3/2)^2, which is (2/3)^(-2)
which means we can rewrite the problem as
%282%2F3%29%5E%28x-2%29+=+%28%282%2F3%29%5E-2%29%5E%282x-1%29
Now, with like bases, the exponents must be equal, and we have
x - 2 = -2(2x - 1)
x - 2 = -4x + 2
5x = 4
x = 4/5

Answer by jrfrunner(365) About Me  (Show Source):