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(x+2)³ Expand log 4x

(x+2)³ Expand log 4x

Calculus: Early Transcendentals
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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The image contains a mathematical expression: "Expand log((x + 2)^3 / 4x)" This is a logarithmic function that involves the expansion of the log of a fraction, where the numerator is \((x + 2)^3\) and the denominator is \(4x\). To expand this logarithmic expression, apply the properties of logarithms: 1. **Quotient Rule**: \(\log(\frac{a}{b}) = \log(a) - \log(b)\) 2. **Power Rule**: \(\log(a^b) = b \cdot \log(a)\) Applying these rules, the expression can be expanded as follows: 1. \(\log((x + 2)^3 / 4x) = \log((x + 2)^3) - \log(4x)\) 2. Apply the power rule: \(\log((x + 2)^3) = 3 \cdot \log(x + 2)\) 3. Expand \(\log(4x)\) using the product rule: \(\log(4x) = \log(4) + \log(x)\) So, the fully expanded expression is: \[3 \cdot \log(x + 2) - \log(4) - \log(x)\]
Transcribed Image Text:The image contains a mathematical expression: "Expand log((x + 2)^3 / 4x)" This is a logarithmic function that involves the expansion of the log of a fraction, where the numerator is \((x + 2)^3\) and the denominator is \(4x\). To expand this logarithmic expression, apply the properties of logarithms: 1. **Quotient Rule**: \(\log(\frac{a}{b}) = \log(a) - \log(b)\) 2. **Power Rule**: \(\log(a^b) = b \cdot \log(a)\) Applying these rules, the expression can be expanded as follows: 1. \(\log((x + 2)^3 / 4x) = \log((x + 2)^3) - \log(4x)\) 2. Apply the power rule: \(\log((x + 2)^3) = 3 \cdot \log(x + 2)\) 3. Expand \(\log(4x)\) using the product rule: \(\log(4x) = \log(4) + \log(x)\) So, the fully expanded expression is: \[3 \cdot \log(x + 2) - \log(4) - \log(x)\]
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