Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Hello, I would like see if I had done this problem right, can you please help me?
Please see attached image
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![**Topic: Converting Logarithmic Equations to Exponential Form**
---
**Instruction: Rewrite as an exponential equation.**
Given:
\[ \ln 6 = x \]
**Solution:**
The natural logarithm function, \(\ln\), is the logarithm to the base \(e\), where \(e\) is approximately equal to 2.71828. To convert the given logarithmic equation into its equivalent exponential form, we use the definition of the natural logarithm:
\[ \ln a = b \Rightarrow e^b = a \]
Using this definition with the given equation \( \ln 6 = x \), we can rewrite it as:
\[ e^x = 6 \]
So, the exponential form of the equation \( \ln 6 = x \) is:
\[ e^x = 6 \]
---
**Explanation:**
Converting logarithmic equations to exponential form is a fundamental skill in algebra. This conversion is useful in solving equations involving logarithms and understanding the relationships between logarithmic and exponential functions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd9e4490e-6c12-4d59-b6bf-c6e024b1a154%2F5efedb24-eaf2-4a62-b00b-3d81fcc13aba%2Fto2td7o_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Topic: Converting Logarithmic Equations to Exponential Form**
---
**Instruction: Rewrite as an exponential equation.**
Given:
\[ \ln 6 = x \]
**Solution:**
The natural logarithm function, \(\ln\), is the logarithm to the base \(e\), where \(e\) is approximately equal to 2.71828. To convert the given logarithmic equation into its equivalent exponential form, we use the definition of the natural logarithm:
\[ \ln a = b \Rightarrow e^b = a \]
Using this definition with the given equation \( \ln 6 = x \), we can rewrite it as:
\[ e^x = 6 \]
So, the exponential form of the equation \( \ln 6 = x \) is:
\[ e^x = 6 \]
---
**Explanation:**
Converting logarithmic equations to exponential form is a fundamental skill in algebra. This conversion is useful in solving equations involving logarithms and understanding the relationships between logarithmic and exponential functions.
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