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Question
\[\lim_{x \to 0} \frac{a^x + b^x - 2}{x}\]
Solution
\[\lim_{x \to 0} \left[ \frac{a^x + b^x - 2}{x} \right]\]
\[ = \lim_{x \to 0} \left[ \frac{a^x - 1 + b^x - 1}{x} \right]\]
\[ = \lim_{x \to 0} \left[ \frac{a^x - 1}{x} \right] + \lim_{x \to 0} \left[ \frac{b^x - 1}{x} \right]\]
\[ = \log a + \log b\]
\[ = \log \left( ab \right)\]
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