دوال ولغارتيمية مفيدة للرياضيات يستفاد منها الطالب في كلية الهندسة

1. Lecture :Suhair Hussein Talib
22
Al-Mustaqbal University
CollegeDepartment of Medical
InstrumentationTechniques
Engineering
First class
Lecture Four
Exponential function and logarithmic function .

2. 1
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The Logarithmic function:
The logarithmic was discovered by Noble man John Napier (1550-1617)
( )
Where y is the logarithm, x is the number, b is the base.
If , we write
Where (ln) is read natural logarithm.
The logarithmic was discovered by Noble man John Napier (1550-1617)
( )
Where y is the logarithm, x is the number, b is the base.
If , we write
Where (ln) is read natural logarithm.
Derivative of the natural logarithm:
( ) ́( )

3. 2
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Example: Find of the following functions:
1- ( )
Sol:
( )
2- ( )
Sol:
( ) ( )
3- ( ) ( )
Sol:
( )
√ ( )
( )
√ ( )
The Exponential function:
Definition: the exponential function is defined as an inverse of natural logarithm,
and denoted by: exp or e , that is:
For ( )

4. 3
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5. 4
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Example: Simplify the following expressions.
1-
2-
3- ( )
4-
5-
6-
7-
Example: Solve for y if: ( )
Sol:
( ) (Take for both sides)
( )

6. 5
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Derivative of the exponential function:
Now, if ( )
Example: Find of the following functions.
1-
( )
2- ( )
( )
( )
3- ( )
The Function
Definition: for
If

7. 6
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Now if ( )
Example: Find of the following functions.
1-
( )
2-
Example

8. 7
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H.W
1.
2. Solve for x if
3. Find
4.