Concept explainers
To find: the logarithmic equation that relates y to x .
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Answer to Problem 85E
Explanation of Solution
Given:
The table:
x | 1 | 2 | 3 | 4 | 5 | 6 |
y | 2.5 | 2.102 | 1.9 | 1.768 | 1.672 | 1.597 |
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 | |
0.916 | 0.743 | 0.642 | 0.570 | 0.514 | 0.468 |
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
That is, equation of line is,
Now, to find b , substitute any point
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
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