PURE MATHEMATICS - Algebra

 

Laws of Exponentials & Logarithms

 

 

Laws

Proofs

Base Change

Simultaneous Equations

x in index

 

 

 

The Laws of Logarithms

 

laws of logarithms

 

 

Proofs

number division and log subtratraction

 

 

change of base proof

 

 

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Changing the Base

 

Remember that the change of base occurs in the term where the base is 'x' or some other variable.

 

 

Example #1

 

logarithm problem#1

 

 

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Simultaneous Equations

 

'Substitution' simultaneous equations are common problems.

 

method:

 

1. first find what x is in terms of y
2. then substitute for x in the other equation
3. solve for y

 

 

Example #1

 

logarithm problem#2

 

 

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Variable in the Index

 

method:

 

1. take logs on both sides

2. move the indices infront of the logs

3. expand the equation

4. collect x-terms to the left

5. sum the numbers to the right

 

 

These problems can be tricky with the amount of arithmetic involved.

 

So make sure you write everything down to make checking your working easier.

 

 

Example #1

 

logarithm problem#3

 

 

 

 

 

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