Solve for the exact value

Question

2^x= 3^x-5

solve for exact value!! thanks

Answer 1

Change the equation into logarithm form:

2^x = 3^x-5

x log 2 = (x - 5) log 3

x (log 2 - log 3) = -5 log 3

x = (-5 log 3)/(log 2/3)