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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Question
![**Solve for \( y \). Give an exact answer.**
\[ 2y - 5 = e^{\ln(20)} \]
\[ y = \boxed{\phantom{answer}} \]
**Explanation:**
To solve for \( y \) in the equation, we start by evaluating the right-hand side:
1. \( e^{\ln(20)} = 20 \) because the exponential function \( e^x \) and the natural logarithm \( \ln(x) \) are inverse functions.
The equation becomes:
\[ 2y - 5 = 20 \]
2. Add 5 to both sides of the equation:
\[ 2y = 25 \]
3. Divide both sides by 2 to solve for \( y \):
\[ y = \frac{25}{2} \]
So, the exact answer for \( y \) is:
\[ y = \boxed{\frac{25}{2}} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0d404c5d-4d55-46c0-aff4-29578c5eba85%2F3c75e91a-5e8e-4dc5-98c5-43f78bcc5451%2Fi9ejt2_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Solve for \( y \). Give an exact answer.**
\[ 2y - 5 = e^{\ln(20)} \]
\[ y = \boxed{\phantom{answer}} \]
**Explanation:**
To solve for \( y \) in the equation, we start by evaluating the right-hand side:
1. \( e^{\ln(20)} = 20 \) because the exponential function \( e^x \) and the natural logarithm \( \ln(x) \) are inverse functions.
The equation becomes:
\[ 2y - 5 = 20 \]
2. Add 5 to both sides of the equation:
\[ 2y = 25 \]
3. Divide both sides by 2 to solve for \( y \):
\[ y = \frac{25}{2} \]
So, the exact answer for \( y \) is:
\[ y = \boxed{\frac{25}{2}} \]
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