# NATURAL LOGARITHMS AND THE NUMBER E

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```					Course: Algebra III/Trig
Unit: Exponential and Logarithmic Functions                                                 Section
Chapter: 11

NATURAL LOGARITHMS AND THE NUMBER E                                                              7
Objective: To find natural logarithms of numbers and solve equations using natural logarithms.

What is e?

Use a calculator to evaluate the formula given for the value of e.

1 1       1          1              1
e = 1+ +    +        +            +                 + ...
1 1! 2 1! 2 ! 3 1! 2 ! 3 ! 4 1! 2 ! 3 ! 4 ! 5

Notes 1:
Using a table of values graph the equation y = e x

x   y

-2

-1

0

1

2

3

What is a natural logarithm?

What is the “lne” equal to?
Example 1:

Use natural logarithms to solve each equation.

a) 1500 = e 0.25 x

b) 122 = 4e 0.25 x

c) 127 = e x !3
STUDENT PRACTICE 11.7

1) 14 = e x             2) 148 = e x + 2

3) 1400 = 7e 0.33 x     4) 10,000 = 15e 2x !3

5) 17 = 3e 0.2x         6) 145 = 5e 0.5 x + 4

```
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