3^2x-1=5^x I am having trouble solving this since the bases are not the same and I am unclear how to use Ln or Log to solve even though I know I...

Hello!

I think your equation is

`3^(2x-1)=5^x,`

not

`3^(2x)-1=5^x.`

For the first option yes, apply `ln` to both sides (they are both positive). It is known (and not hard) that `ln(a^b)=b*ln(a).`

Here we obtain `(2x-1)*ln(3)=x*ln(5).`

It is a linear equation for x, group like terms:

`x*(2ln(3)-ln(5))=ln(3),`  so

`x=(ln(3))/(2ln(3)-ln(5)) approx 1.869.`

This is the answer for the first option.

I believe the second option cannot be solved exactly, although it has exactly one root and it is in (0, 1).