problem is solve the inequality:

2^(2x-1)<3^(3x-2)

2 to the 2x-1 power<3 to the 3x-2 power

i have already:

1) took ln of 2 and 3

**(2x-1)ln2<(3x-2)ln3**
2) factored

**2x*ln(2)-ln(2)<3x*ln(3)-2ln(3)**
3) added ln2 to both sides

**2x*ln(2)<3x*ln(3)+ln(2)-2ln(3)**
I am stuck as to what to do next i know i must isolate the x but dont see how it will work and still be able to come up with the answer provided by a online solver.

**To isolate x, you need x on one side.**

Subtract 3xln3 from both sides, then factor out x next.

Finally divide both sides by the single remaining multiplier of x

Archie Meade
answer is

**x<(ln(2)-2ln(3)) / (2ln(2)-3ln(3))** **please any help would be great!!!!! please if you could explain thank you**