# How do you graph -2 ln x?

##### 1 Answer
Apr 30, 2017

Start with the graph of $y = \ln \left(x\right)$. Note that $\ln \left(1\right) = 0$, $\ln \left(e\right) = 1$, $\ln \left({e}^{2}\right) = 2$, $\ln \left(\frac{1}{e}\right) = - 1$, and so on.

This means we have points at $\left(\frac{1}{e} ^ 2 , - 2\right) , \left(\frac{1}{e} , - 1\right) \left(1 , 0\right) , \left(e , 1\right) , \left({e}^{2} , 2\right)$, and so on:

$y = \ln x$
graph{lnx [-5.48, 26.55, -7.48, 8.54]}

Multiplying $\ln x$ by $- 1$ will flip the graph over the $x$ axis:

$y = - \ln x$
graph{-lnx [-3.75, 28.28, -7.29, 8.73]}

Multiplying $- \ln x$ by $2$ will cause the point $\left({e}^{2} , - 2\right)$ to become $\left({e}^{2} , - 4\right)$. The graph will "get larger," or rise quicker.

$y = - 2 \ln x$
graph{-2lnx [-8.35, 37.26, -11.87, 10.94]}