Question

How do you solve `5^(x-2) = 3^(3x+2)`?

Answer 1

I found `-3.2116`

Explanation:

We can take the natural log of both sides:
`ln(5)^(x-2)=ln(3)^(3x+2)`
We use the property of the logs:
`logx^y=ylogx`
`(x-2)ln(5)=(3x+2)ln(3)`
Rearrange:
`xln5-2ln5=3xln3+2ln3`
`x(ln5-3ln3)=2ln5+2ln3`
`x=(2ln5+2ln3)/(ln5-3ln3)=-3.2116`