find the value of x:

5 power x-2 multiplied with 3 power 2x – 4 is equal to 5.

give me the answer with check please.

Hi friend,

hope you know logarithms basic theory as it is requiered to solve this question.
Answer :-
given,
5^(x-2) X 3^(2x-4) = 5
or  3^(2x-4) =5/5^(x-2)
or 3^(2x-4) = 5^(1-x+2)
or  ln3^(2x-4)= ln5^(1-x+2)
or  (2x-4)ln3=(1-x+2)ln5
or 2x-4 = 4.8 -1.6  (since value of ln3=1 and value of ln5=1.6 approx)
or 0.4x=8.8
or x=22.
hope you got your answer.
please feel free to comment back if you know something else about this problem.