Answer
$-\infty$
Work Step by Step
Find the limit $\lim\limits_{x \to 3^{+}}log_{10}(x^{2}-5x+6)$
This is quadratic equation in the powers of 2 with roots
$(x-2)$$(x-3)$.
$\lim\limits_{x \to 3^{+}}log_{10}(x^{2}-5x+6)=\lim\limits_{x \to 3^{+}}log_{10}(x-2)(x-3)$
The limit of the logarithm base 10 of $x$ when $x$ approaches zero from the positive side (0+) is minus infinity. This implies
$\lim\limits_{x \to 3^{+}}log_{10}(x^{2}-5x+6)=-\infty$
