Express as a sum or difference of logarithms without exponents. 5 4 X log c 4_7 y'z What is the equivalent sum or difference of logarithms? (Simplify your answer. Use integers or fractions for any numbers in the expression.)
Express as a sum or difference of logarithms without exponents. 5 4 X log c 4_7 y'z What is the equivalent sum or difference of logarithms? (Simplify your answer. Use integers or fractions for any numbers in the expression.)
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
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Chapter1: Functions And Models
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![### Express as a Sum or Difference of Logarithms without Exponents
$$\log_c \sqrt[4]{\frac{x^5}{y^4z^7}}$$
### What is the equivalent sum or difference of logarithms?
(Simplify your answer. Use integers or fractions for any numbers in the expression.)
[ ]
---
**Explanation:**
The given expression pertains to logarithmic properties and rules for simplification. Specifically, it asks for the conversion of the logarithmic expression to a sum or difference of logarithms while removing exponents.
To solve this, you would typically apply the following logarithmic rules:
1. **Power Rule**: \(\log_b(x^y) = y \log_b(x)\)
2. **Quotient Rule**: \(\log_b\left(\frac{x}{y}\right) = \log_b(x) - \log_b(y)\)
3. **Product Rule**: \(\log_b(xy) = \log_b(x) + \log_b(y)\)
Additionally, we need to convert the fourth root to a fractional exponent before applying these properties.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa3230e3d-dd38-497e-8c1e-7c1c5570828c%2F1c2213a7-c62f-4c7b-8231-3ee45ec01388%2Frv72kcj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Express as a Sum or Difference of Logarithms without Exponents
$$\log_c \sqrt[4]{\frac{x^5}{y^4z^7}}$$
### What is the equivalent sum or difference of logarithms?
(Simplify your answer. Use integers or fractions for any numbers in the expression.)
[ ]
---
**Explanation:**
The given expression pertains to logarithmic properties and rules for simplification. Specifically, it asks for the conversion of the logarithmic expression to a sum or difference of logarithms while removing exponents.
To solve this, you would typically apply the following logarithmic rules:
1. **Power Rule**: \(\log_b(x^y) = y \log_b(x)\)
2. **Quotient Rule**: \(\log_b\left(\frac{x}{y}\right) = \log_b(x) - \log_b(y)\)
3. **Product Rule**: \(\log_b(xy) = \log_b(x) + \log_b(y)\)
Additionally, we need to convert the fourth root to a fractional exponent before applying these properties.
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