Question

How do you solve `3^(2x−1) = 5^(2−3x)`?

Answer 1

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`