Homework Help is Here – Start Your Trial Now!
Math
Calculus
L(x) = In(x)+log,(x)

L(x) = In(x)+log,(x)

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
See similar textbooks
icon
Related questions
Question

FInd the derivative of the image below

The function presented is \( L(x) = \ln(x) + \log_5(x) \). ### Explanation: - **\(\ln(x)\)**: This represents the natural logarithm of \(x\), which is the logarithm to the base \(e\), where \(e\) is approximately equal to 2.71828. - **\(\log_5(x)\)**: This term represents the logarithm of \(x\) with base 5. ### Graph/Diagram Explanation: The expression combines two different types of logarithms. When visualizing such a function on a graph: - The curve will showcase how both terms contribute to the overall value of \(L(x)\). - As \(x\) increases, both \(\ln(x)\) and \(\log_5(x)\) increase, but at different rates due to their different bases. - The graph will typically only be defined for \(x > 0\) since logarithms are not defined for zero or negative values. This function can be used to demonstrate the effects of different logarithmic bases on the behavior of logarithmic functions.
Transcribed Image Text:The function presented is \( L(x) = \ln(x) + \log_5(x) \). ### Explanation: - **\(\ln(x)\)**: This represents the natural logarithm of \(x\), which is the logarithm to the base \(e\), where \(e\) is approximately equal to 2.71828. - **\(\log_5(x)\)**: This term represents the logarithm of \(x\) with base 5. ### Graph/Diagram Explanation: The expression combines two different types of logarithms. When visualizing such a function on a graph: - The curve will showcase how both terms contribute to the overall value of \(L(x)\). - As \(x\) increases, both \(\ln(x)\) and \(\log_5(x)\) increase, but at different rates due to their different bases. - The graph will typically only be defined for \(x > 0\) since logarithms are not defined for zero or negative values. This function can be used to demonstrate the effects of different logarithmic bases on the behavior of logarithmic functions.
Expert Solution
Concept:

Used formulas :

ddx(logax) = 1x ln a

ln x = loge xloge e = ln e = 1ln 5 =1.61

steps

Step by step

Solved in 2 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS