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.

Thomas · Accepted Answer · 2012-10-02 15:00:39Z

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:

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

answered Oct 2 '12 at 15:00

Thomas
10.8k21338

Madrit Zhaku · Answer 2 · 2012-10-02 15:05:04Z

up vote 1 down vote

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

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

answered Oct 2 '12 at 15:05

Madrit Zhaku
1

2 Answers