${lim}_{x \to 0} \frac{a^{x} + b^{x} - 2}{x}$

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Solution

${lim}_{x \to 0} \frac{a^{x} + b^{x} - 2}{x}$

$= {lim}_{x \to 0} \frac{a^{m x} - 1}{x} + {lim}_{x \to 0} \frac{b^{x} - 1}{x}$

$= l o g a + l o g b$

$= l o g (a b)$

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