2^2x=16 show all the steps

To solve the equation 2^(2x) = 16, we need to isolate the variable x.

1. Take the log base 2 of both sides to eliminate the exponent:
log₂(2^(2x)) = log₂(16)
2x = log₂(16)

2. Use the property of logarithms that states logₐ(a) = 1 to simplify the equation:
2x = 4

3. Divide both sides by 2 to solve for x:
x = 2

Therefore, the solution to the equation 2^(2x) = 16 is x = 2.