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 = 

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Example of e

loge10  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  = (x+1)
3x (1.95) = (x+1)
2.48 x = (x+1)
(2.48-1) x = 1
1.48 x = 1
x 0.647

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