Entir Write the expression as a sum and/or difference of logarithms. Express powers as factors. x(x+6) log (x +5)5 , x>0 ober - No ..... x(x+6) log (x+5)5 (Simplify your answer.)
Entir Write the expression as a sum and/or difference of logarithms. Express powers as factors. x(x+6) log (x +5)5 , x>0 ober - No ..... x(x+6) log (x+5)5 (Simplify your answer.)
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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![**Transcription of Educational Content**
**Instructions:**
Write the expression as a sum and/or difference of logarithms. Express powers as factors.
**Problem Statement:**
\[
\log \left[ \frac{x(x+6)}{(x+5)^5} \right], \quad x > 0
\]
**Step for Simplification:**
\[
\log \left[ \frac{x(x+6)}{(x+5)^5} \right] = \quad \_\_\_\_\_ \quad (\text{Simplify your answer.})
\]
**Explanation:**
The given problem involves expressing the logarithm of a fraction as a combination of logarithms. The task is to simplify the expression using the properties of logarithms such as:
1. **Logarithm of a quotient**:
\[
\log\left(\frac{a}{b}\right) = \log(a) - \log(b)
\]
2. **Logarithm of a product**:
\[
\log(ab) = \log(a) + \log(b)
\]
3. **Logarithm of a power**:
\[
\log(a^b) = b \cdot \log(a)
\]
Utilize these properties to break down and express the given logarithmic expression into a sum and/or difference form where powers are handled properly.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F11c3e735-47a2-4be2-bcf0-76944b0744ea%2F9ba820e8-93e2-4300-89d3-368728e5d69b%2Ff6okkiro_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Transcription of Educational Content**
**Instructions:**
Write the expression as a sum and/or difference of logarithms. Express powers as factors.
**Problem Statement:**
\[
\log \left[ \frac{x(x+6)}{(x+5)^5} \right], \quad x > 0
\]
**Step for Simplification:**
\[
\log \left[ \frac{x(x+6)}{(x+5)^5} \right] = \quad \_\_\_\_\_ \quad (\text{Simplify your answer.})
\]
**Explanation:**
The given problem involves expressing the logarithm of a fraction as a combination of logarithms. The task is to simplify the expression using the properties of logarithms such as:
1. **Logarithm of a quotient**:
\[
\log\left(\frac{a}{b}\right) = \log(a) - \log(b)
\]
2. **Logarithm of a product**:
\[
\log(ab) = \log(a) + \log(b)
\]
3. **Logarithm of a power**:
\[
\log(a^b) = b \cdot \log(a)
\]
Utilize these properties to break down and express the given logarithmic expression into a sum and/or difference form where powers are handled properly.
Expert Solution
Step 1
Use property of logarithms
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