Answer
$log_{10}(x^{2}+10x+24)$
Work Step by Step
We know that $log_{b}xy=log_{b}x+log_{b}y$ (where $x$, $y$, and $b$ are positive real numbers and $b\ne1$).
Therefore, $log_{10}(x+4)+log_{10}(x+6)=log_{10}((x+4)(x+6))$.
We can use the FOIL method to further simplify.
$log_{10}((x+4)(x+6))=log_{10}(x^{2}+6x+4x+24)=log_{10}(x^{2}+10x+24)$.
