a=3^b

 

b^a-a^b=0

 

a.b=?

Do you know the answer? Is it 18?

nah it 42. its always 42.

answer is "9" but ı dont know how it is..

what's the dot between the a and b in the last equation supposed to be?

 

it's that multiplication?

dot product since it would appear to be scalar values it works out to be multiplication.

 

i don't even know what he's supposed to be working out. if he wants help he should tell us what to look ffor.

Okay so we know that: a=3^b and b^a=a^b, and you want a proof that ab=9. Is that right?

I found ab to be something like: 9.721577574

with a = 5.974795378

and b = 1.627097994

I have the imrpression that the OP has erroneously described the problem. I have been looking into this problem and as it is formulated, it only can be tackled by means of iterative numerical methods for root finding and then an answer, like raptor has given pops up, but I suspect this is not the answer the OP is expecting.