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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![The image presents a mathematical problem that prompts the viewer to find the value of a logarithm. The question is as follows:
"Find the value of the logarithm."
\[ \ln \left( \frac{1}{e} \right) \]
On the right side, there is a space with an equal sign indicating where the solution should be placed:
\[ \ln \left( \frac{1}{e} \right) = \text{☐} \]
**Explanation of the Solution:**
To solve \( \ln \left( \frac{1}{e} \right) \), we use the logarithmic identity:
\[ \ln \left( \frac{1}{e} \right) = \ln(e^{-1}) = -\ln(e) \]
Since the natural logarithm of \( e \) (i.e., \(\ln(e)\)) is 1:
\[ -\ln(e) = -1 \]
Thus, the value is \(-1\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbac5cd56-9885-4a25-8e51-dfc1bb78a29e%2F9e12e0b3-bb78-4365-916b-17129740a0f5%2F2kpfm55_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The image presents a mathematical problem that prompts the viewer to find the value of a logarithm. The question is as follows:
"Find the value of the logarithm."
\[ \ln \left( \frac{1}{e} \right) \]
On the right side, there is a space with an equal sign indicating where the solution should be placed:
\[ \ln \left( \frac{1}{e} \right) = \text{☐} \]
**Explanation of the Solution:**
To solve \( \ln \left( \frac{1}{e} \right) \), we use the logarithmic identity:
\[ \ln \left( \frac{1}{e} \right) = \ln(e^{-1}) = -\ln(e) \]
Since the natural logarithm of \( e \) (i.e., \(\ln(e)\)) is 1:
\[ -\ln(e) = -1 \]
Thus, the value is \(-1\).
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