Solve for x over the real numbers:
log(x^2) = log^2(x)
Subtract log^2(x) from both sides:
log(x^2) - log^2(x) = 0
Transform log(x^2) - log^2(x) into a polynomial with respect to log(x):
2 log(x) - log^2(x) = 0
Factor log(x) and constant terms from the left hand side:
-log(x) (log(x) - 2) = 0
Multiply both sides by -1:
log(x) (log(x) - 2) = 0
Split into two equations:
log(x) - 2 = 0 or log(x) = 0
Add 2 to both sides:
log(x) = 2 or log(x) = 0
Cancel logarithms by taking exp of both sides:
x = e^2 or log(x) = 0
Cancel logarithms by taking exp of both sides:
Answer: |x = e^2 or x = 1
