Answer
$ln(x)+\frac{1}{2}ln(x^{2}+5)$
Work Step by Step
Use the rule that $log(ab)=log(a)+log(b)$ to expand the logarithm into $ln(x)+ln\sqrt{x^{2}+5}$. Finally, use the fact that $\sqrt x = x^{\frac{1}{2}}$ to change the $ln\sqrt{x^{2}+5}$ into $ln((x^{2}+5)^{\frac{1}{2}})$. and then use the rule that $log(x^{n}) = nlog(x)$ to simplify it to $\frac{1}{2}ln(x^{2}+5)$. Combining that logarithm with $ln(x)$ gives you $ln(x)+\frac{1}{2}ln(x^{2}+5)$.
