Solving logarithims

Question

Solve 4^2x-5=0.5^2-2x

Answer 1

4^2x-5 = 0.5^2-2x

 

Now 4 = 2² and 0.5 = 1/2 = 2^-1:

 

(2²)^2x-5 = (2^-1)^2-2x

2^4x-10 = 2^-2+2x

 

Since the two terms are equal and have the same base, their exponents are equal:

 

4x - 10 = -2 + 2x

2x = 8

x = 4