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Use the properties of logarithms to expand each expression in terms of simpler logarithms. Assume that all variable expressions denote positive numbers. 13. | 45 36, log ()- log ( - log ( atb 7, 49 nction )- log ( 15ac,

Use the properties of logarithms to expand each expression in terms of simpler logarithms. Assume that all variable expressions denote positive numbers. 13. | 45 36, log ()- log ( - log ( atb 7, 49 nction )- log ( 15ac,

Algebra and Trigonometry (6th Edition)
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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**Expanding Logarithmic Expressions** Use the properties of logarithms to expand each expression in terms of simpler logarithms. Assume that all variable expressions denote positive numbers. Expression: \[ \log \left( \frac{a^5 \sqrt{b}}{a+b} \right) = \underline{\quad} \cdot \log(\phantom{x}) + \underline{\quad} \cdot \log(\phantom{x}) - \log(\phantom{x}) \] **Answers** | Step | Answer | |------|--------| | 1 | - | | 2 | - | | 3 | - | | 4 | - | **Instructions and Explanation:** 1. Identify the expression inside the log and break it into factors. 2. Apply the logarithm power rule: \(\log(x^n) = n \cdot \log(x)\). 3. Apply the logarithm product rule: \(\log(x \cdot y) = \log(x) + \log(y)\). 4. Apply the logarithm quotient rule: \(\log\left(\frac{x}{y}\right) = \log(x) - \log(y)\). Fill out the blanks with the appropriate expressions using these rules. Remember to adjust exponents when applying the power rule and ensure all variable expressions remain positive.
Transcribed Image Text:**Expanding Logarithmic Expressions** Use the properties of logarithms to expand each expression in terms of simpler logarithms. Assume that all variable expressions denote positive numbers. Expression: \[ \log \left( \frac{a^5 \sqrt{b}}{a+b} \right) = \underline{\quad} \cdot \log(\phantom{x}) + \underline{\quad} \cdot \log(\phantom{x}) - \log(\phantom{x}) \] **Answers** | Step | Answer | |------|--------| | 1 | - | | 2 | - | | 3 | - | | 4 | - | **Instructions and Explanation:** 1. Identify the expression inside the log and break it into factors. 2. Apply the logarithm power rule: \(\log(x^n) = n \cdot \log(x)\). 3. Apply the logarithm product rule: \(\log(x \cdot y) = \log(x) + \log(y)\). 4. Apply the logarithm quotient rule: \(\log\left(\frac{x}{y}\right) = \log(x) - \log(y)\). Fill out the blanks with the appropriate expressions using these rules. Remember to adjust exponents when applying the power rule and ensure all variable expressions remain positive.
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