SOLUTION: Use properties of exponents to solve: 3^(x-2)81^(x)=(1/3)^(x-3) Im lost on this problem

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Use properties of exponents to solve: 3^(x-2)81^(x)=(1/3)^(x-3) Im lost on this problem      Log On


   

Question 308159: Use properties of exponents to solve:
3^(x-2)81^(x)=(1/3)^(x-3)

Im lost on this problem
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Use properties of exponents to solve:
3^(x-2)81^(x)=(1/3)^(x-3)
------------
81 = 3^4
1/3 = 3^-1
-----------
3%5E%28x-2%2981%5E%28x%29=%281%2F3%29%5E%28x-3%29
3%5E%28x-2%293%5E%284x%29=+3%5E%283-x%29
3%5E%285x-2%29+=+3%5E%283-x%29
5x-2 = 3-x
6x = 5
x = 5/6