Let \( b > 0, b \neq 1 \). Which of the following must be true if \( y = \log_b(x) \)? Check all that apply. - [ ] \( y = b^x \) - [ ] \( \frac{dy}{dx} = b^x \ln(b) \) - [ ] \( \frac{dy}{dx} = \frac{1}{\ln(b)} \left( \frac{1}{x} \right) \) - [ ] \( x = b^y \) - [ ] \( y = \frac{1}{\ln(b)} \ln(x) \)
Let \( b > 0, b \neq 1 \). Which of the following must be true if \( y = \log_b(x) \)? Check all that apply. - [ ] \( y = b^x \) - [ ] \( \frac{dy}{dx} = b^x \ln(b) \) - [ ] \( \frac{dy}{dx} = \frac{1}{\ln(b)} \left( \frac{1}{x} \right) \) - [ ] \( x = b^y \) - [ ] \( y = \frac{1}{\ln(b)} \ln(x) \)
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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![Let \( b > 0, b \neq 1 \). Which of the following must be true if \( y = \log_b(x) \)?
Check all that apply.
- [ ] \( y = b^x \)
- [ ] \( \frac{dy}{dx} = b^x \ln(b) \)
- [ ] \( \frac{dy}{dx} = \frac{1}{\ln(b)} \left( \frac{1}{x} \right) \)
- [ ] \( x = b^y \)
- [ ] \( y = \frac{1}{\ln(b)} \ln(x) \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0d29bdc9-47d1-4ff2-b560-e93fe0e23599%2F1f120e9f-81b6-45cb-a44d-100b86015a40%2F60yje9.jpeg&w=3840&q=75)
Transcribed Image Text:Let \( b > 0, b \neq 1 \). Which of the following must be true if \( y = \log_b(x) \)?
Check all that apply.
- [ ] \( y = b^x \)
- [ ] \( \frac{dy}{dx} = b^x \ln(b) \)
- [ ] \( \frac{dy}{dx} = \frac{1}{\ln(b)} \left( \frac{1}{x} \right) \)
- [ ] \( x = b^y \)
- [ ] \( y = \frac{1}{\ln(b)} \ln(x) \)
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