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Question
\[\lim_{x \to 2} \frac{x - 2}{\log_a \left( x - 1 \right)}\]
Solution
\[\lim_{x \to 2} \left[ \frac{x - 2}{\log_a \left( x - 1 \right)} \right]\]
Let x = 2 + h
x → 2
∴ h → 0
\[ = \log a \lim_{h \to 0} \left[ \frac{h}{\log \left( 1 + h \right)} \right]\]
\[ = \log a \times 1\]
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