Answer
$log_{10}(10x^{2}+20)$
Work Step by Step
The product property of logarithms tells us that $log_{b}xy=log_{b}x+log_{b}y$ (where x, y, and, b are positive real numbers and $b\ne1$).
Therefore, $log_{10}5+log_{10}2+log_{10}(x^{2}+2)= log_{10}(5\times2\times(x^{2}+2))=log_{10}(10x^{2}+20)$.
