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
![**Instruction:**
Combine into one logarithm. Do not simplify. Assume all expressions are defined.
\[ 3 \log(7m) + 4 \log(m + 7) = \log\left( \text{___________} \right) \]
**Answers:**
| Answers | Answer |
|---------|--------------------------------------------|
| | |
**Explanation:**
The question asks to combine the logarithmic expressions \(3 \log(7m)\) and \(4 \log(m + 7)\) into a single logarithm. This can be done using the properties of logarithms, specifically the product property:
1. Use the power rule \(\log_b(x^n) = n\log_b(x)\) to rewrite each term:
- \(3 \log(7m)\) becomes \(\log((7m)^3)\)
- \(4 \log(m + 7)\) becomes \(\log((m + 7)^4)\)
2. Use the product property \(\log_b(x) + \log_b(y) = \log_b(xy)\) to combine:
- \(\log((7m)^3) + \log((m + 7)^4) = \log((7m)^3 \cdot (m + 7)^4)\)
Thus, the combined logarithmic expression within the log function is:
\[\log\left((7m)^3 \cdot (m + 7)^4\right)\]
There is no graph or diagram in the image.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8b5cafd2-a634-4d0f-8315-5dac4bc10fac%2Ff12119bd-3f29-4c45-9ab7-24b1a2b3a321%2Fkvstr3d.jpeg&w=3840&q=75)
Transcribed Image Text:**Instruction:**
Combine into one logarithm. Do not simplify. Assume all expressions are defined.
\[ 3 \log(7m) + 4 \log(m + 7) = \log\left( \text{___________} \right) \]
**Answers:**
| Answers | Answer |
|---------|--------------------------------------------|
| | |
**Explanation:**
The question asks to combine the logarithmic expressions \(3 \log(7m)\) and \(4 \log(m + 7)\) into a single logarithm. This can be done using the properties of logarithms, specifically the product property:
1. Use the power rule \(\log_b(x^n) = n\log_b(x)\) to rewrite each term:
- \(3 \log(7m)\) becomes \(\log((7m)^3)\)
- \(4 \log(m + 7)\) becomes \(\log((m + 7)^4)\)
2. Use the product property \(\log_b(x) + \log_b(y) = \log_b(xy)\) to combine:
- \(\log((7m)^3) + \log((m + 7)^4) = \log((7m)^3 \cdot (m + 7)^4)\)
Thus, the combined logarithmic expression within the log function is:
\[\log\left((7m)^3 \cdot (m + 7)^4\right)\]
There is no graph or diagram in the image.
Expert Solution
Step 1
Given logarithmic equation
We have to simplify by using
Log a + Log b = Log(ab)
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