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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![## Solving Logarithmic Equations
**Example Problem:**
Solve the following equation for \( x \):
\[ 7 - \ln x = 0 \]
### Solution Steps:
1. **Isolate the logarithmic term:**
To isolate \( \ln x \), move 7 to the other side of the equation:
\[ \ln x = 7 \]
2. **Exponentiate both sides:**
To solve for \( x \), exponentiate both sides with the base \( e \) (Euler's number, approximately 2.71828):
\[ x = e^7 \]
### Final Answer:
\[
x = e^7
\]
> Type an exact answer in the provided input box.
For practice, make sure you understand how to isolate the logarithmic term and how to exponentiate correctly to solve for \( x \). Remember, the natural logarithm function \( \ln x \) is the inverse of the exponential function \( e^x \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb3c4489a-e4bd-4ff1-89b5-d5833f06911e%2F28a93acf-9605-42aa-93d4-b6dea379316a%2F5e38zkt_processed.png&w=3840&q=75)
Transcribed Image Text:## Solving Logarithmic Equations
**Example Problem:**
Solve the following equation for \( x \):
\[ 7 - \ln x = 0 \]
### Solution Steps:
1. **Isolate the logarithmic term:**
To isolate \( \ln x \), move 7 to the other side of the equation:
\[ \ln x = 7 \]
2. **Exponentiate both sides:**
To solve for \( x \), exponentiate both sides with the base \( e \) (Euler's number, approximately 2.71828):
\[ x = e^7 \]
### Final Answer:
\[
x = e^7
\]
> Type an exact answer in the provided input box.
For practice, make sure you understand how to isolate the logarithmic term and how to exponentiate correctly to solve for \( x \). Remember, the natural logarithm function \( \ln x \) is the inverse of the exponential function \( e^x \).
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