Limit finding without L'Hospital's rule – math.stackexchange.com

Limit finding without L'Hospital's rule – math.stackexchange.com

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I have to find: $$\lim_{x\to0}{\frac{\ln(1+e^x)-\ln2}{x}}$$ and I want to calculate it without using L'Hospital's rule. With L'Hospital's I know that it gives $1/2$. Any ideas?

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