LOGARITHM HANDWRITTEN NOTES FOR NDA 2022 | HELP4NDA

LOGARITHM 

In this unit we are going to be looking at logarithms. 

However, before we can deal with logarithms we need to revise indices. 

This is because logarithms and indices are closely related, and in order to understand logarithms a good knowledge of indices is required. 

We know that 16 = 2*4 Here, the number 4 is the power. Sometimes we call it an exponent. Sometimes we call it an index.

 In the expression 2*4 , the number 2 is called the base. Example We know that 64 = 8*2 . In this example 2 is the power, or exponent, or index. The number 8 is the base.

What is a logarithm ? Consider the expression 16 = 2*4 . 

Remember that 2 is the base, and 4 is the power. An alternative, yet equivalent, way of writing this expression is log2 16 = 4. This is stated as ‘log to base 2 of 16 equals 4’. 

We see that the logarithm is the same as the power or index in the original expression. It is the base in the original expression which becomes the base of the logarithm. 

The two statements 16 = 2*4 log2 16 = 4 are equivalent statements. If we write either of them, we are automatically implying the other. 

Example If we write down that 64 = 8*2 then the equivalent statement using logarithms is log8 64 = 2. 

Example If we write down that log3 27 = 3 then the equivalent statement using powers is 3 *3 = 27. 

So the two sets of statements, one involving powers and one involving logarithms are equivalent. In the general case we have:

if x = a* n then equivalently log a x = n

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