Subtract 2 from both sides:
(log(2 x^2))/(log(2)) = 1
Multiply both sides by log(2):
log(2 x^2) = log(2)
Cancel logarithms by taking exp of both sides:
2 x^2 = 2
Divide both sides by 2:
x^2 = 1
Take the square root of both sides:
Answer: |x =1 or x = -1