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Question
\[\lim_{x \to 0} \frac{5^x + 3^x + 2^x - 3}{x}\]
Solution
\[\lim_{x \to 0} \left[ \frac{5^x + 3^x + 2^x - 3}{x} \right]\]
\[ = \lim_{x \to 0} \left[ \frac{5^x - 1}{x} + \frac{3^x - 1}{x} + \frac{2^x - 1}{x} \right]\]
\[ = \log \left( 5 \right) + \log \left( 3 \right) + \log \left( 2 \right)\]
\[ = \log \left( 5 \times 3 \times 2 \right)\]
\[ = \log 30\]
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