What is the property called that says that $a^x = a^y$ iff $x = y$?

Question

I was just wondering why two numbers $a^x$ and $a^y$ are equal only if $x = y$ ? Which power-law is this?

Answer 1

It is true only if $a>0$ and $a\ne 1$ and , in this case, it is a consequence of the fact that the function $y:\mathbb{R}\to\mathbb{R} \quad y=a^x$ ,is one-to-one.

Answer 2

This is general property of injective function: $$f(x)=f(y)\Longrightarrow x=y$$ In this case your function is the exponent function $f(x)=a^x$, $(a\ne 1, a>0)$