# How do you graph y=e^(ln x)?

May 9, 2018

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

#### Explanation:

The natural logarithm function, if considered as a real-valued function of a real variable, is the inverse function of the exponential function, leading to the identities:
${e}^{\setminus \ln x} = x \setminus q \quad \setminus \textrm{\mathmr{if}} x > 0 \setminus q \quad {e}^{\setminus \ln x} = x \setminus q \quad \setminus \textrm{\mathmr{if}} x > 0$
$\setminus \ln \left({e}^{x}\right) = x$
Like all logarithms, the natural logarithm maps multiplication into addition:
$\setminus \ln \left(x y\right) = \setminus \ln x + \setminus \ln y$

from natural logarithm.