PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
8th Edition
ISBN: 9781337904285
Author: Larson
Publisher: CENGAGE L
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Chapter 3.3, Problem 54E

a)

To determine

To graph:

The given two functions on the same viewing rectangle.

a)

Expert Solution
Check Mark

Answer to Problem 54E

The required graph is:

  PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS), Chapter 3.3, Problem 54E , additional homework tip 1

Explanation of Solution

Given:

Two logarithmic functions:

  y1=ln(xx+3), y2=12lnx−ln(x+3)

Calculation:

Upon entering the given two equations on the TI-84 Plus calculator and then graphing them, we get the required graph as shown below:

  PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS), Chapter 3.3, Problem 54E , additional homework tip 2

b)

To determine

To create:

A table of values for the given functions and the graphs using the ‘table’ feature of the calculator.

b)

Expert Solution
Check Mark

Answer to Problem 54E

The required table is:

  PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS), Chapter 3.3, Problem 54E , additional homework tip 3

Explanation of Solution

Given:

Two logarithmic functions:

  y1=ln(xx+3), y2=12lnx−ln(x+3)

Upon using the ‘table’ feature of the calculator, we get the tables for the given two functions as shown below:

  PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS), Chapter 3.3, Problem 54E , additional homework tip 4

c)

To determine

To conclude:

What do the graphs in part (a) and tables in part (b) conclude about the given two functions? Verify the conclusion algebraically.

c)

Expert Solution
Check Mark

Answer to Problem 54E

Both the functions have the same graph and the same table. Hence both the functions are equivalent to each other.

Explanation of Solution

Given:

Two logarithmic functions:

  y1=ln(xx+3), y2=12lnx−ln(x+3)

From the graphs in part (a) and the tables in part (b), we can see that both the functions are equivalent to each others.

Algebraic verification:

Upon simplifying the first function using properties of logarithm, we get the second function.

  y1=ln(xx+3)y1=ln(x)−ln(x+3) (Subtraction property of logarithms)y1=ln(x12)−ln(x+3) (Rewriting radical to exponent form)y1=12ln(x)−ln(x+3) (Exponent property of logarithms)y1=y2

Hence, we have verified algebraically that both the functions are the same.

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Chapter 3.3, Problem 53E
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Chapter 3.3, Problem 55E

Chapter 3 Solutions

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)

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Prob. 27CTCh. 3 - Prob. 28CTCh. 3 - Prob. 29CTCh. 3 - Prob. 30CTCh. 3 - Prob. 1STPCh. 3 - Prob. 2STPCh. 3 - Prob. 3STPCh. 3 - Prob. 4STPCh. 3 - Prob. 5STPCh. 3 - Prob. 6STPCh. 3 - Prob. 7STPCh. 3 - Prob. 8STPCh. 3 - Prob. 9STPCh. 3 - Prob. 10STPCh. 3 - Prob. 11STPCh. 3 - Prob. 12STPCh. 3 - Prob. 13STPCh. 3 - Prob. 14STPCh. 3 - Prob. 15STPCh. 3 - Prob. 16STPCh. 3 - Prob. 17STPCh. 3 - Prob. 18STPCh. 3 - Prob. 19STPCh. 3 - Prob. 20STPCh. 3 - Prob. 21STPCh. 3 - Prob. 22STPCh. 3 - Prob. 23STPCh. 3 - Prob. 24STPCh. 3 - Prob. 25STPCh. 3 - Prob. 26STP
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Implicit Differentiation with Transcendental Functions; Author: Mathispower4u;https://www.youtube.com/watch?v=16WoO59R88w;License: Standard YouTube License, CC-BY
How to determine the difference between an algebraic and transcendental expression; Author: Study Force;https://www.youtube.com/watch?v=xRht10w7ZOE;License: Standard YouTube License, CC-BY