да Use the change-of-base formula to determine an expression in terms of a common logarithm and a natural logarithm equivalent to logs (2). (x) = log₂ (x) log (a)
да Use the change-of-base formula to determine an expression in terms of a common logarithm and a natural logarithm equivalent to logs (2). (x) = log₂ (x) log (a)
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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I need help with the natural logarithm please.
![### Change-of-Base Formula for Logarithms
The change-of-base formula allows you to evaluate logarithms with any base using common logarithms (base 10) or natural logarithms (base e). The formula is given by:
\[
\log_a(x) = \frac{\log_b(x)}{\log_b(a)}
\]
where \(b\) is the new base, often 10 or e.
#### Exercise A
Determine the expression for \(\log_5(2)\) using common logarithms and natural logarithms.
- **Common Logarithm:**
\[
\log_5(2) = \frac{\log(2)}{\log(5)}
\]
- **Natural Logarithm:**
\[
\log_5(2) = \frac{\ln(2)}{\ln(5)}
\]
#### Exercise B
Determine the expression for \(\log_9(4)\) using:
- **Common Logarithm:**
\[
\log_9(4) = \frac{\log(4)}{\log(9)}
\]
- **Natural Logarithm:**
\[
\log_9(4) = \frac{\ln(4)}{\ln(9)}
\]
#### Exercise C
Determine the expression for \(\log_7(11)\) using:
- **Common Logarithm:**
\[
\log_7(11) = \frac{\log(11)}{\log(7)}
\]
- **Natural Logarithm:**
\[
\log_7(11) = \frac{\ln(11)}{\ln(7)}
\]
#### Exercise D
Determine the expression for \(\log_6(4)\) using:
- **Common Logarithm:**
\[
\log_6(4) = \frac{\log(4)}{\log(6)}
\]
- **Natural Logarithm:**
\[
\log_6(4) = \frac{\ln(4)}{\ln(6)}
\]
These exercises illustrate how you can express logarithms for any base using more familiar logarithms.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc28712d6-8cc5-484b-ae89-313fccbcf9cb%2F72e820cf-7f36-4f06-9553-36e8273b3075%2Ferkq6k8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Change-of-Base Formula for Logarithms
The change-of-base formula allows you to evaluate logarithms with any base using common logarithms (base 10) or natural logarithms (base e). The formula is given by:
\[
\log_a(x) = \frac{\log_b(x)}{\log_b(a)}
\]
where \(b\) is the new base, often 10 or e.
#### Exercise A
Determine the expression for \(\log_5(2)\) using common logarithms and natural logarithms.
- **Common Logarithm:**
\[
\log_5(2) = \frac{\log(2)}{\log(5)}
\]
- **Natural Logarithm:**
\[
\log_5(2) = \frac{\ln(2)}{\ln(5)}
\]
#### Exercise B
Determine the expression for \(\log_9(4)\) using:
- **Common Logarithm:**
\[
\log_9(4) = \frac{\log(4)}{\log(9)}
\]
- **Natural Logarithm:**
\[
\log_9(4) = \frac{\ln(4)}{\ln(9)}
\]
#### Exercise C
Determine the expression for \(\log_7(11)\) using:
- **Common Logarithm:**
\[
\log_7(11) = \frac{\log(11)}{\log(7)}
\]
- **Natural Logarithm:**
\[
\log_7(11) = \frac{\ln(11)}{\ln(7)}
\]
#### Exercise D
Determine the expression for \(\log_6(4)\) using:
- **Common Logarithm:**
\[
\log_6(4) = \frac{\log(4)}{\log(6)}
\]
- **Natural Logarithm:**
\[
\log_6(4) = \frac{\ln(4)}{\ln(6)}
\]
These exercises illustrate how you can express logarithms for any base using more familiar logarithms.
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