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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Graphing Logarithmic Functions In Exercises 13–20, sketch the graph of the function. See Example 1.

y = 4 ln ( x 3 )

To determine

To graph: The function y=4ln(x3).

Explanation

Given Information:

The provided function is y=4ln(x3).

Graph:

Consider the function, y=4ln(x3)

The natural logarithmic function is defined only for positive values, so the domain of the function, y=4ln(x3) is x3>0 or x>3.

As the domain is x>3, then take the value of x greater than 3.

To draw the graph of y=4ln(x3), first compute the value of y for different values of x.

Compute the value of y at x=4 by substituting x=4 in the equation y=4ln(x3) as,

y(4)=4ln(43)=4ln(1)=40=0

Compute the value of y at x=5 by substituting x=5 in the equation y=4ln(x3) as,

y(5)=4ln(53)=4ln(2)=40.693=2.772

Compute the value of y at x=6 by substituting x=6 in the equation y=4ln(x3) as,

y(6)=4ln(63)=4ln(3)=41.099=4

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