Question

3 to the power log4= 4 to the power log3

Answer 1

3 to the power log4= 4 to the power log3
taking log on both side 

log4log3=log3l0g4
and then solve it by product rule 

Answer 2

LHS - - - - - - - - RHS
------- - - - - - - - ---------
3^log4 - - - - - - 4^log3
=log(3^log4) --=log(4^log3)
[..taking log on both sides.]
=log4×log3 - - - =log3×log4
.
.
So.. LHS=RHS.
Hope this is ur required answer.