Limx #8594;0 #160;8x 2xx=limx #8594;0 #160;8x 1x 2x 1x=log #160;8 log #160;2=log #160;82=log #160;4 ...

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Fundamental Laws of Logarithms

lim x → 08 x-...

Question

$\lim_{x \to 0} \frac{8^{x} - 2^{x}}{x}$

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Solution

$\lim_{x \to 0} [\frac{8^{x} - 2^{x}}{x}] = \lim_{x \to 0} [\frac{(8^{x} - 1)}{x} - \frac{(2^{x} - 1)}{x}] = \log (8) - \log (2) = \log (\frac{8}{2}) = \log 4$

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