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True or false: For any real number b > 1, and any real numbers > 0 and y > 0, it must be true that: log, (y) = log, (a)+logs (y) O False O True

True or false: For any real number b > 1, and any real numbers > 0 and y > 0, it must be true that: log, (y) = log, (a)+logs (y) O False O True

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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**Logarithmic Identity Verification** **Question:** Determine the validity of the logarithmic identity for any real number \( b > 1 \), and any real numbers \( x > 0 \) and \( y > 0 \). Evaluate if the following equation holds true: \[ \log_b(xy) = \log_b(x) + \log_b(y) \] **Options:** - False - True **Explanation:** This equation represents a fundamental property of logarithms, known as the logarithm product rule. According to this rule, the logarithm of a product is equal to the sum of the logarithms. The assertion is valid due to the fact that logarithms convert multiplication into addition.
Transcribed Image Text:**Logarithmic Identity Verification** **Question:** Determine the validity of the logarithmic identity for any real number \( b > 1 \), and any real numbers \( x > 0 \) and \( y > 0 \). Evaluate if the following equation holds true: \[ \log_b(xy) = \log_b(x) + \log_b(y) \] **Options:** - False - True **Explanation:** This equation represents a fundamental property of logarithms, known as the logarithm product rule. According to this rule, the logarithm of a product is equal to the sum of the logarithms. The assertion is valid due to the fact that logarithms convert multiplication into addition.
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Step 1: True or false

Yes, the statement 

is true for any real number  and any real numbers  and . This is a fundamental property of logarithms and is known as the product rule for logarithms.


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