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Question
\[\lim_{x \to 0} \frac{3^{2 + x} - 9}{x}\]
Solution
\[\lim_{x \to 0} \left[ \frac{3^{2 + x} - 9}{x} \right]\]
\[ = \lim_{x \to 0} \left[ \frac{3^2 \cdot 3^x - 3^2}{x} \right]\]
\[ = 3^2 \lim_{x \to 0} \left[ \frac{3^x - 1}{x} \right]\]
\[ = 9 \log \left( 3 \right)\]
\[ = 9 \log_e 3\]
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