Single Variable Calculus, Chapter 7, 7.3-1, Section 7.3-1, Problem 46

Determine the limit $\displaystyle \lim_{x \to 2^-} \log_3 \left( 8x - x^4 \right)$
By using table of values as $x$ approaches 2 from the left.

$
\begin{array}{|c|c|}
\hline\\
x & y \\
\hline\\
1.99 & -0.8929\\
1.999 & -2.3180\\
1.9999 & -3.7481\\
1.99999 & -5.1788\\
\hline
\end{array}
$

We set that the as $x$ approaches 2 from the left, $y$ becomes a negatively large value, and by substituting 2 in the equation. We get...
$\displaystyle \lim_{x \to 2^-} \log_5 \left[ 8(2) - (2)^4 \right] = \lim_{x \to 2^-} \log_5 0$
And by the property of log
$\displaystyle \lim_{x \to 0^+} \log_a x = - \infty$
Therefore, $\displaystyle \lim_{x \to 2^-} \log_5 \left( 8x - x^4 \right) = -\infty$