## Intermediate Algebra (12th Edition)

{$x$|$x\gt0$,$x\ne1$}
For all positive numbers $a$, where $a\ne1$, and all positive numbers $x$, we know that $y=log_{a}x$ means the same as $x=a^{y}$. Therefore, $log_{x}x=1$ means the same as $x^{1}=x$. We know that $x$ will be a solution for any positive number other than 1, because $x^{1}=x$ will hold for all positive numbers.