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%3D or False: If y=lne, then y'= 1? Explain

%3D or False: If y=lne, then y'= 1? Explain

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...
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Question
**Title: Understanding Logarithmic Functions** **Topic: Logarithmic Identity Exploration** **Question:** True or False: If \( y = \ln e \), then \( y = 1 \)? Explain. --- **Explanation:** To evaluate whether this statement is true or false, we need to recall the basic property of logarithms: The natural logarithm is defined as the inverse of the exponential function. Specifically, for any positive number \( a \), the expression \( \ln a \) is the power to which \( e \) must be raised to equal \( a \). Given the statement: \( y = \ln e \). - We know that the base of the natural logarithm is \( e \). - Therefore, \( \ln e = 1 \) because \( e^1 = e \). Thus, the statement "If \( y = \ln e \), then \( y = 1 \)" is **True**. Make sure to apply these properties correctly when working with logarithmic and exponential functions to validate equations and solve problems effectively.
Transcribed Image Text:**Title: Understanding Logarithmic Functions** **Topic: Logarithmic Identity Exploration** **Question:** True or False: If \( y = \ln e \), then \( y = 1 \)? Explain. --- **Explanation:** To evaluate whether this statement is true or false, we need to recall the basic property of logarithms: The natural logarithm is defined as the inverse of the exponential function. Specifically, for any positive number \( a \), the expression \( \ln a \) is the power to which \( e \) must be raised to equal \( a \). Given the statement: \( y = \ln e \). - We know that the base of the natural logarithm is \( e \). - Therefore, \( \ln e = 1 \) because \( e^1 = e \). Thus, the statement "If \( y = \ln e \), then \( y = 1 \)" is **True**. Make sure to apply these properties correctly when working with logarithmic and exponential functions to validate equations and solve problems effectively.
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