How to evaluate this formula

Question

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.

Thanks.

Answer 1

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:

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

Answer 2

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

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