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

Answer 1

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) [-23.1, 23.15, 46.2, 46.2]}

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

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

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Answer 2

To graph ( y = 5 \ln(3x) ), follow these steps:

  1. Identify key points:
    • Find the vertical asymptote: ( 3x = 0 ) implies ( x = 0 ). So, there's a vertical asymptote at ( x = 0 ).
    • Determine behavior as ( x \rightarrow 0^+ ) and ( x \rightarrow +\infty ).
  2. Plot points:
    • Choose values for ( x ) to the left and right of ( x = 0 ) to see the behavior.
    • Calculate corresponding ( y ) values using the equation.
  3. Draw the graph:
    • Connect the points smoothly, considering the behavior around the asymptote.

Remember, the graph will be a logarithmic curve that approaches the vertical asymptote at ( x = 0 ), and it will never intersect or go below the x-axis.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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