Solve the following exponent equation by expressing each sid

Solve the following exponent equation by expressing each side as a power of the same base and then 16^x + 4 = 256^x - 6 The solution set is

Solution

Lets bring the base to 2, and then equate RHS and LHS:

16^x+4 = 256^x-6
2^4(x+4) = 2^8(x-6)

4x+16 = 8x-48
64 = 4x
x=16
So. x=16