I've recently begun studying for the GRE, and this was the problem:

(1/2)^a=(1/3)^b

These were the answer choices (I'm not sure if they are important for this, so I'm including them just in case):

Which is true?

a<b<0

b>a>0

b<a<0

b<0<a

a<0<b

The solution to this problem began with:

"From (1/2)^a=(1/3)^b, we know that 2^a=3^b"

However, I'm not sure how "we know" this. I tried setting a=2 and seeing if (1/2)^a and 2^a were the same, but I got 1/4 and 4. Any clarification would be greatly appreciated, as questions like these seem to come up a lot in practice and if there are assumptions I can make, I want to know them Thanks!