How do you graph #-2 ln x#?

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Answer 1 · 2017-04-30T18:57:39

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]}