How do you solve 3^(2x−1) = 5^(2−3x)?

1 Answer
Nov 28, 2015

I found: x=0.61454

Explanation:

Take the natural log of both sides:
ln3^(2x-1)=ln5^(2-3x)
use the property of logs:
logx^a=alogx
(2x-1)ln3=(2-3x)ln5
2(ln3)x-ln3=2ln5-3(ln5)x
collect x:
x[2(ln3)+3(ln5)]=2ln5+ln3
x[7.02554]=4.31748
x=4.31748/7.02554=0.61454