# If $x>0$ and $x^a=x^b$ can one assume that $a=b$?

If $x>0$ and $x^a=x^b$ can one assume that $a=b$? The answer says it's not right. I've tried coming up with a counter-example but keep failing.

• No, $1^0=1^1=1$, but $0\neq 1$. – Dietrich Burde May 16 '16 at 19:15
$$\log(x^a) = \log(x^b)\Longrightarrow a\log x = b\log x \Longrightarrow (b-a)\log x = 0.$$