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Question
\[\lim_{x \to 0} \frac{a^x + b^x + c^x - 3}{x}\]
Solution
\[\lim_{x \to 0} \left[ \frac{a^n + b^n + c^n - 3}{x} \right]\]
\[ = \lim_{x \to 0} \left[ \frac{\left( a^n - 1 \right)}{x} + \frac{\left( b^n - 1 \right)}{x} + \frac{\left( c^n - 1 \right)}{x} \right]\]
\[ = \log a + \log b + \log c\]
\[ = \log \left( abc \right)\]
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