SOLUTION: Solve: 5^2x-3 = 6^3x

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Solve: 5^2x-3 = 6^3x      Log On


   

Question 92175: Solve: 5^2x-3 = 6^3x
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Solve: 5^2x-3 = 6^3x
:
Assume you mean:
5%5E%28%282x-3%29%29 = 6%5E%283x%29
:
ln%285%5E%28%282x-3%29%29%29 = ln%286%5E%283x%29%29; nat log of both sides
:
%282x-3%29%2Aln%285%29 = %283x%29%2Aln%286%29; log equiv of exponents
:
1.609%282x-3%29 = %283x%29%2A1.792
:
3.219x - 4.828 = 5.375x
:
-4.827 = 5.375x - 3.219x
:
2.156x = -4.827
:
x = -4.827%2F2.156
:
x = -2.239