Evaluate the following limit: _ x 0 log(1+x) 3^ x -1 - Vidyadip

Question

Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow0}\frac{\text{log}(1+\text{x})}{3^{\text{x}}-1 }$

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Answer

$\lim\limits_{\text{x}\rightarrow0}\frac{\text{log}(1+\text{x})}{3^{\text{x}}-1 }$
$=\lim\limits_{\text{x}\rightarrow0}\frac{\text{log}(1+\text{x})}{\text{x}}\times\frac{1}{\lim\limits_{\text{x}\rightarrow0}\frac{3^\text{x}-1}{\text{x}}}$
$=\frac{1}{\text{log3}}$

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