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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Question
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### Logarithms: Problem-Solving Example
**Problem:**
Given that \( \log_a 5 = 0.699 \) and \( \log_a 11 = 1.041 \), find \( \log_a 55 \).
**Options:**
A. Cannot be found from the given information.
B. 0.728
C. 0.489
D. 1.740
**Solution:**
To find \( \log_a 55 \), we use the logarithm property:
\[ log_a (xy) = \log_a x + \log_a y \]
Since 55 can be written as the product of 5 and 11:
\[ \log_a 55 = \log_a (5 \times 11) = \log_a 5 + \log_a 11 \]
Given the values:
\[ \log_a 5 = 0.699 \]
\[ \log_a 11 = 1.041 \]
Adding these logarithms:
\[ \log_a 55 = 0.699 + 1.041 = 1.740 \]
Therefore, the correct answer is:
**D. 1.740**
---
**Note:** This problem requires the application of basic logarithmic properties to solve. It tests the understanding of how to manipulate and combine logarithmic expressions effectively.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F227fd297-25c6-41a3-8d4d-df25e1639e4d%2F972e9e5d-ebb4-4900-a31a-1ead2f510988%2Fpyyjeq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:---
### Logarithms: Problem-Solving Example
**Problem:**
Given that \( \log_a 5 = 0.699 \) and \( \log_a 11 = 1.041 \), find \( \log_a 55 \).
**Options:**
A. Cannot be found from the given information.
B. 0.728
C. 0.489
D. 1.740
**Solution:**
To find \( \log_a 55 \), we use the logarithm property:
\[ log_a (xy) = \log_a x + \log_a y \]
Since 55 can be written as the product of 5 and 11:
\[ \log_a 55 = \log_a (5 \times 11) = \log_a 5 + \log_a 11 \]
Given the values:
\[ \log_a 5 = 0.699 \]
\[ \log_a 11 = 1.041 \]
Adding these logarithms:
\[ \log_a 55 = 0.699 + 1.041 = 1.740 \]
Therefore, the correct answer is:
**D. 1.740**
---
**Note:** This problem requires the application of basic logarithmic properties to solve. It tests the understanding of how to manipulate and combine logarithmic expressions effectively.
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