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logarithm. That is, each answer should contain only one log (or In) expression. a. log, (x) + log,2(y) log_2(xy) Preview b. log, (æ) – log,(y) = 0.60206 x - 0.60206 y - Preview c. 4logs(x) + logs(y) 4/3*log_2(x)+1 Preview d. In(x)+ ln(y) - In(2) = Preview

logarithm. That is, each answer should contain only one log (or In) expression. a. log, (x) + log,2(y) log_2(xy) Preview b. log, (æ) – log,(y) = 0.60206 x - 0.60206 y - Preview c. 4logs(x) + logs(y) 4/3*log_2(x)+1 Preview d. In(x)+ ln(y) - In(2) = Preview

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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4.8

### Logarithm Simplification Exercises Rewrite each of the following expressions as a single logarithm. Each answer should contain only one log (or ln) expression. --- **a.** \( \log_2(x) + \log_2(y) \) - **Answer:** \( \log_2(xy) \) ✓ Explanation: This uses the logarithm product rule, which states that \( \log_b(M) + \log_b(N) = \log_b(MN) \). --- **b.** \( \log_4(x) - \log_4(y) \) - **Incorrect Attempt:** \( 0.60206x - 0.60206y \) ✕ Explanation: The correct simplification is \( \log_4\left(\frac{x}{y}\right) \) based on the logarithm quotient rule, \( \log_b(M) - \log_b(N) = \log_b\left(\frac{M}{N}\right) \). --- **c.** \( 4\log_8(x) + \log_8(y) \) - **Incorrect Attempt:** \( \frac{4}{3}\log_2(x) + 1 \) ✕ Explanation: First, use the power rule, \( a\log_b(M) = \log_b(M^a) \), and then the product rule. The correct expression is \( \log_8(x^4 \cdot y) \). --- **d.** \( \ln(x) + \ln(y) - \ln(z) \) - **Incorrect Attempt:** ✕ Explanation: Use the product and quotient rules for natural logarithms. The correct expression is \( \ln\left(\frac{xy}{z}\right) \). --- These exercises demonstrate how to consolidate multiple logarithmic expressions into a single expression using logarithmic rules.
Transcribed Image Text:### Logarithm Simplification Exercises Rewrite each of the following expressions as a single logarithm. Each answer should contain only one log (or ln) expression. --- **a.** \( \log_2(x) + \log_2(y) \) - **Answer:** \( \log_2(xy) \) ✓ Explanation: This uses the logarithm product rule, which states that \( \log_b(M) + \log_b(N) = \log_b(MN) \). --- **b.** \( \log_4(x) - \log_4(y) \) - **Incorrect Attempt:** \( 0.60206x - 0.60206y \) ✕ Explanation: The correct simplification is \( \log_4\left(\frac{x}{y}\right) \) based on the logarithm quotient rule, \( \log_b(M) - \log_b(N) = \log_b\left(\frac{M}{N}\right) \). --- **c.** \( 4\log_8(x) + \log_8(y) \) - **Incorrect Attempt:** \( \frac{4}{3}\log_2(x) + 1 \) ✕ Explanation: First, use the power rule, \( a\log_b(M) = \log_b(M^a) \), and then the product rule. The correct expression is \( \log_8(x^4 \cdot y) \). --- **d.** \( \ln(x) + \ln(y) - \ln(z) \) - **Incorrect Attempt:** ✕ Explanation: Use the product and quotient rules for natural logarithms. The correct expression is \( \ln\left(\frac{xy}{z}\right) \). --- These exercises demonstrate how to consolidate multiple logarithmic expressions into a single expression using logarithmic rules.
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