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Answer 1 · 2017-12-16T12:16:14

As shown below:

The first thing to consider what #lnx# looks like:

#y = lnx#:

graph{lnx [-4.58, 15.42, -4.2, 5.8]}

So hence #y = 4lnx# represents #lnx# being stretch in the #y# axis by a scale factor of #4#.

#y = ln4x #:
graph{ln(4x) [-5.29, 14.71, -3.8, 6.2]}

With the same asymptote of #x=0#

enter image source here

Green - #4lnx #
Red - #lnx #

It is also the graph of #lnx^4 # using our log laws.