# Question #2641d

Feb 6, 2018

$\frac{1}{x}$

#### Explanation:

Remember that ${a}^{b} = {e}^{b \cdot \ln a}$.

Here, $a = x$, and $b = - 1$.

The above equation becomes ${e}^{- 1 \cdot \ln x}$.

Using the above property of powers, this simplifies to:

${x}^{-} 1$

$= \frac{1}{x}$

Feb 6, 2018

The answer is $= \frac{1}{x}$

#### Explanation:

Let $y = {e}^{- \ln x}$

Taking the logarithms on both sides,

$\ln y = \ln \left({e}^{- \ln x}\right)$

$= - \ln x$

$= \ln 1 - \ln x$

$= \ln \left(\frac{1}{x}\right)$

As,

$\ln y = \ln \left(\frac{1}{x}\right)$

$y = \frac{1}{x}$