How do you graph #y=5ln(3x)#?

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Answer 1 · 2016-08-24T02:06:21

y is defined for #x>0#; y has a zero at #x=1/3#;
#y -> -oo# as #x-> 0# (See graphs below)

#y=5ln(3x)#

Since #lna# is defined for #a>0 -> y# is defined for #3x>0#
Hence for #x>0#

Since #lna=0# for #a=1 -> y =0# for #3x =1#
Hence y has a zero at #x=1/3#

For the purposes of graphing function #y# the #5# has the effect of amplifying the magnitude of #ln3x# five times.

graph{5ln(3x) [-46.2, 46.2, -23.1, 23.15]}

In the region closer to #(1/3, 0)#

graph{5ln(3x) [-1.915, 1.927, -0.941, 0.983]}