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Mathematics Magazine for Grades 1-12  

 

 

Grade 12

   
Theory:

RULES OF LOGARITHMS

Let a be a positive number such that a does not equal 1, let n be a real number, and let u and v be positive real numbers.

Logarithmic Rule 1: Loga (uv) = Loga(u) + Loga(v)

Logarithmic Rule 2:  

Logarithmic Rule 3:

Problems with Solutions:

1.       

Solution:

We have

 

.

2.        Evaluate the integral

 

Solution:

3.        Use direct substitution to solve the integral

Solution:

We substitute . .

 

4.        Evaluate the integral

Solution: We substitute .  .

5.        Use a trigonometric substitution to evaluate the integral

Solution:

We substitute . 

Proposed Problems:

Simplify the following expressions:

1.                    E= .

2.                   

3.             
 
 

Read more on the written version of the publication.