Concept explainers
To find: the logarithmic equation that relates y to x .
Answer to Problem 83E
Explanation of Solution
Given:
The table:
x | 1 | 2 | 3 | 4 | 5 | 6 |
y | 1 | 1.189 | 1.316 | 1.414 | 1.495 | 1.565 |
Concept Used:
Slope of a line:
The slope of line passing through two point
Slope intercept form of equation of line is
Construct a new table by taking the natural logarithms of the x and y values in the given table.
0 | 0.693 | 1.099 | 1.386 | 1.609 | 1.792 | |
0 | 0.173 | 0.275 | 0.346 | 0.402 | 0.447 |
Now plot each point
Now, choose any two points to determine the slope of the line.
So, using the points
Now, from the slope-intercept form of line, the equation of line is:
Where
From the above graph, it is clear that the y -intercept of line is 0. That is,
Thus, the equation of line is:
Conclusion:
The logarithmic equation that relates y to x is
Chapter 3 Solutions
EBK PRECALCULUS W/LIMITS
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning