Lim_x→ 08^x 2^x/x =lim_x→ 0(8^x 1) (2^x 1)/x =lim_x→ 08^x 1/x lim_x→ 02^x 1/x =log 8 log 2=log ( 8/2 ) =log 4 ...

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Standard Limits to Remove Indeterminate Form

lim x → 08x-2...

Question

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

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Solution

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

$= {lim}_{x \to 0} \frac{(8^{x} - 1) - (2^{x} - 1)}{x}$

$= {lim}_{x \to 0} \frac{8^{x} - 1}{x} - {lim}_{x \to 0} \frac{2^{x} - 1}{x}$

$= l o g 8 - l o g 2 = l o g (\frac{8}{2})$

$= l o g 4$

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