Question

How do you graph `-2 ln x`?

Answer 1

Start with the graph of `y=ln(x)`. Note that `ln(1)=0`, `ln(e)=1`, `ln(e^2)=2`, `ln(1/e)=-1`, and so on.

This means we have points at `(1/e^2,-2),(1/e,-1)(1,0),(e,1),(e^2,2)`, and so on:

`y=lnx`
graph{lnx [-5.48, 26.55, -7.48, 8.54]}

Multiplying `lnx` by `-1` will flip the graph over the `x` axis:

`y=-lnx`
graph{-lnx [-3.75, 28.28, -7.29, 8.73]}

Multiplying `-lnx` by `2` will cause the point `(e^2,-2)` to become `(e^2,-4)`. The graph will "get larger," or rise quicker.

`y=-2lnx`
graph{-2lnx [-8.35, 37.26, -11.87, 10.94]}