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How can I evaluate $1/e^{\ln(x)}$? I really don't have experience on this and appreciate if you can explain it to me.


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$e^{\ln x}=x$ by definition – user39572 Oct 2 '12 at 14:56
up vote 3 down vote accepted

By definition you have that $\ln(x) = y$ if and ony if $e^y = x$. Hence you would have that $$ e^{\ln(x)} = x. $$ So in your example:

$$ \frac{1}{e^{\ln(x)}} = \frac{1}{x}. $$

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Implement the formula: $a^{\log_a b}=b$, and $\ln x=\log_e x$ we have:

$\frac{1}{e^{\ln (x)}}=\frac{1}{e^{\log_e (x)}}=\frac{1}{x}$

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