E

Definition Of E

e is the base of the natural logarithm. Its value is constant and is equivalent to 2.71828182845904523536...

More About e

e is also called Euler's number.
ln(e^x) = x
In terms of limit, e is defined as e = example of e

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Example of e

loge 10 example of e 2.30258 where e is the base of the given logarithm.

Solved Example on e

Ques: Solve the equation by using natural logarithms.
53x = 7(x + 1)

Choices:

A. x = 0.647
B. x = 1.647
C. x = 0.947
D. x = 1.947
Correct Answer: A

Solution:

Step 1: Consider 53x = 7(x + 1)
Step 2: Apply log on both sides,
ln 53x = ln 7(x + 1)
Step 3: 3x ln 5 = (x+1) ln 7
3x example of e = (x+1)
3x (1.95) = (x+1)
2.48 x = (x+1)
(2.48-1) x = 1
1.48 x = 1
x 0.647

Quick Summary

e is the base of the natural logarithm.
e is approximately 2.71828.
ln(e^x) = x

\[ e = \lim_{n \to \infty} (1 + \frac{1}{n})^n \]

🍎 Teacher Insights

Emphasize the relationship between e and exponential growth/decay. Use real-world examples to illustrate its applications.

🎓 Prerequisites

Logarithms
Exponents
Limits

Check Your Knowledge

Q1: What is the approximate value of e?

3.14 1.62 2.72 4.20

Q2: What is ln(e)?

0 1 e Undefined

Frequently Asked Questions

Q: Why is 'e' important?
A: It appears in many areas of mathematics, including calculus, exponential growth, and statistics. It is fundamental to understanding natural logarithms and exponential functions.

Q: What is the natural logarithm?
A: The natural logarithm, denoted as ln(x), is the logarithm to the base e.

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