(a)
To Explain: The definition of the logarithmic function
(a)
Explanation of Solution
Let
To prove:
Proof:
Consider
Equating the powers on both sides,
Therefore, it is one to one and
Here
Thus, the logarithm of x in base b is written for
(b)
To find: The domain of
(b)
Answer to Problem 33E
The domain of
Explanation of Solution
Since the logarithmic function is the inverse of the exponential function, the domain of logarithmic function is the range of exponential function.
The exponential function is always positive so logarithmic function is not definedfor negative numbers or for zero.
Therefore, the domain of the logarithmic function
(c)
To find: The range of
(c)
Answer to Problem 33E
Solution:
The range of
Explanation of Solution
Since the logarithmic function is the inverse of the exponential function, the range of logarithmic function is the domain of exponential function.
The exponential function is defined for all real numbers so logarithmic function can take any real number.
Therefore, the range of the logarithmic function
(d)
To sketch: The graph of the function
(d)
Explanation of Solution
Graph:
Use online graph calculator and draw the graph of the function
Chapter 1 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced Edition
- 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