Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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#29 please explain
![### Logarithmic and Exponential Functions
This section covers questions on logarithmic and exponential functions. We'll explore properties and evaluate expressions using given logarithmic facts.
#### Questions 28-34: Evaluate Logarithmic and Exponential Expressions
**28.** \( \log_{4} 16 \)
**29.** \( \log_{9} 3 \)
**30.** If \( f(x) = \ln(x) \), find \( f(\sqrt{e}) \).
**31.** If \( f(x) = \log(x) \), find \( f(10^{-7}) \).
**32.** If \( f(x) = \ln(x) \), find \( f(\sqrt{e}) \).
**33.** If \( f(x) = e^x \), find \( f(\ln 3) \).
**34.** If \( f(x) = 10^x \), find \( f(\log 2) \).
#### Problems 35-36: Evaluate Logarithms Using Given Properties
*Key Properties and Facts:*
- \(\log_a x = 3.1\)
- \(\log_a y = 1.8\)
- \(\log_a z = 2.2\)
**35.** Evaluate the following using logarithmic properties:
(a) \( \log_a (xy) \)
(c) \( \log_a (x^4) \)
**36.** Evaluate the following using logarithmic properties:
(b) \( \log_a \left(\frac{x}{z}\right) \)
(d) \( \log_a \left(\sqrt[3]{y}\right) \)
### Understanding the Concepts
Each question requires an understanding of the key properties of logarithms and the relationship between logarithms and exponents:
- Logarithmic identities such as \(\log_a (xy) = \log_a x + \log_a y\).
- Understanding how to apply logarithms to evaluate expressions like exponentials.
- Recognizing the inverse relationship: \( f(x) = e^x \) and \( f(x) = \ln(x) \) are inverse functions.
These exercises are designed to reinforce the manipulation and evaluation of logarithmic and exponential expressions using algebraic properties.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faeb06b0e-8341-4861-846e-a0416daf2b6f%2Ff7f527c1-d257-417e-9670-14a838ad9b85%2Fp0jk49o_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Logarithmic and Exponential Functions
This section covers questions on logarithmic and exponential functions. We'll explore properties and evaluate expressions using given logarithmic facts.
#### Questions 28-34: Evaluate Logarithmic and Exponential Expressions
**28.** \( \log_{4} 16 \)
**29.** \( \log_{9} 3 \)
**30.** If \( f(x) = \ln(x) \), find \( f(\sqrt{e}) \).
**31.** If \( f(x) = \log(x) \), find \( f(10^{-7}) \).
**32.** If \( f(x) = \ln(x) \), find \( f(\sqrt{e}) \).
**33.** If \( f(x) = e^x \), find \( f(\ln 3) \).
**34.** If \( f(x) = 10^x \), find \( f(\log 2) \).
#### Problems 35-36: Evaluate Logarithms Using Given Properties
*Key Properties and Facts:*
- \(\log_a x = 3.1\)
- \(\log_a y = 1.8\)
- \(\log_a z = 2.2\)
**35.** Evaluate the following using logarithmic properties:
(a) \( \log_a (xy) \)
(c) \( \log_a (x^4) \)
**36.** Evaluate the following using logarithmic properties:
(b) \( \log_a \left(\frac{x}{z}\right) \)
(d) \( \log_a \left(\sqrt[3]{y}\right) \)
### Understanding the Concepts
Each question requires an understanding of the key properties of logarithms and the relationship between logarithms and exponents:
- Logarithmic identities such as \(\log_a (xy) = \log_a x + \log_a y\).
- Understanding how to apply logarithms to evaluate expressions like exponentials.
- Recognizing the inverse relationship: \( f(x) = e^x \) and \( f(x) = \ln(x) \) are inverse functions.
These exercises are designed to reinforce the manipulation and evaluation of logarithmic and exponential expressions using algebraic properties.
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