How do you graph ln(x)?

Jun 28, 2018

Reflect the graph of ${e}^{x}$ in the line $y = x$...

Explanation:

First think about how you can graph ${e}^{x}$

Note that $e \approx 2.71828182844$, so ${e}^{x}$ is a smooth exponential curve passing through:

$\left(0 , 1\right)$

$\left(1 , e\right) \approx \left(1 , 2.718\right)$

$\left(2 , {e}^{2}\right) \approx \left(2 , 7.389\right)$

$\left(3 , {e}^{3}\right) \approx \left(3 , 20.0855\right)$

...

$\left(- 1 , {e}^{- 1}\right) \approx \left(- 1 , 0.3679\right)$

$\left(- 2 , {e}^{- 2}\right) \approx \left(- 2 , 0.1353\right)$

$\left(- 3 , {e}^{- 3}\right) \approx \left(- 3 , 0.0498\right)$

...

So it looks like this:
graph{e^x [-11.04, 8.96, -1.28, 8.72]}

To get the graph of its inverse $\ln \left(x\right)$, we can reflect this graph in the diagonal line $y = x$ to get:
graph{ln x [-5.04, 14.96, -6.96, 3.04]}