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
![**Problem Statement**
Use the Change of Base Formula to evaluate \( \log_{14}(39) \). (Round your answer to three decimal places.)
[Answer Box]
**Solution**
The answer provided is 8.
**Explanation**
To evaluate the logarithm \( \log_{14}(39) \) using the Change of Base Formula, which states:
\[
\log_{b}(a) = \frac{\log_{c}(a)}{\log_{c}(b)}
\]
We can use common logarithms (base 10) or natural logarithms (base e) for \( c \). Here, we calculate:
\[
\log_{14}(39) = \frac{\log_{10}(39)}{\log_{10}(14)}
\]
By calculating the values, we get the answer rounded to three decimal places. However, the provided calculation results in the number 8, which might be an error since the precise mathematical computation usually results in a value between \(1\) and \(2\). It’s essential to verify calculations with a calculator or software to ensure accuracy.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F51b63292-92ab-4e1d-b8e0-da3dc6733332%2F5e885c6e-efa4-4b51-8dff-bec2be072d20%2F5s058cg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement**
Use the Change of Base Formula to evaluate \( \log_{14}(39) \). (Round your answer to three decimal places.)
[Answer Box]
**Solution**
The answer provided is 8.
**Explanation**
To evaluate the logarithm \( \log_{14}(39) \) using the Change of Base Formula, which states:
\[
\log_{b}(a) = \frac{\log_{c}(a)}{\log_{c}(b)}
\]
We can use common logarithms (base 10) or natural logarithms (base e) for \( c \). Here, we calculate:
\[
\log_{14}(39) = \frac{\log_{10}(39)}{\log_{10}(14)}
\]
By calculating the values, we get the answer rounded to three decimal places. However, the provided calculation results in the number 8, which might be an error since the precise mathematical computation usually results in a value between \(1\) and \(2\). It’s essential to verify calculations with a calculator or software to ensure accuracy.
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