## Precalculus (10th Edition)

$x \gt 10$.
The definition of the logarithmic function says that $y=\log_a{x}$ if and only if $a^y=x$. Also, $a\gt0,a\ne1$ and $x\gt0$. By the definition of the logarithmic function we can only take the logarithm of a positive number, hence in the expression $\log_a {A}$ or $\ln {A}$, $A$ must be positive. Hence $\frac{x}{2}-5\gt 0\\\frac{x}{2}\gt 5\\x \gt 10$.