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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Write the logarithmic expression as a single logarithm with coefficient 1, and simplify as much as possible.
![**Transcription of Logarithmic Expression Problem**
**Problem:**
Write the logarithmic expression:
\[
\log_9 20,412 - \log_9 7 - \log_9 4
\]
**Options:**
- ☐ \(\log_9 20,423\)
- ☐ 3
- ☐ 20,401
- ☐ \(\log_9 571,536\)
**Solution Explanation:**
The given expression is a subtraction of logarithms, which can be simplified using the logarithm property:
\[
\log_b a - \log_b c = \log_b \left( \frac{a}{c} \right)
\]
Thus, the expression becomes:
\[
\log_9 \left( \frac{20,412}{7 \times 4} \right)
\]
Calculation:
1. Compute \( 7 \times 4 = 28 \).
2. Divide \( 20,412 \) by \( 28 \), resulting in \( 729 \).
3. Therefore, the expression simplifies to:
\[
\log_9 729
\]
This matches one of the options if simplified or calculated correctly.
Note: The solution requires evaluating the options based on the simplified expression.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2f1b8d52-12f4-4831-bc71-189b57bb4a76%2Fdae2f63a-9b97-430e-a3f3-4cc9db1799d5%2F2lbbz9e_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Transcription of Logarithmic Expression Problem**
**Problem:**
Write the logarithmic expression:
\[
\log_9 20,412 - \log_9 7 - \log_9 4
\]
**Options:**
- ☐ \(\log_9 20,423\)
- ☐ 3
- ☐ 20,401
- ☐ \(\log_9 571,536\)
**Solution Explanation:**
The given expression is a subtraction of logarithms, which can be simplified using the logarithm property:
\[
\log_b a - \log_b c = \log_b \left( \frac{a}{c} \right)
\]
Thus, the expression becomes:
\[
\log_9 \left( \frac{20,412}{7 \times 4} \right)
\]
Calculation:
1. Compute \( 7 \times 4 = 28 \).
2. Divide \( 20,412 \) by \( 28 \), resulting in \( 729 \).
3. Therefore, the expression simplifies to:
\[
\log_9 729
\]
This matches one of the options if simplified or calculated correctly.
Note: The solution requires evaluating the options based on the simplified expression.
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