570 WordsAug 11, 20153 Pages

INDICES, SURDS & LOGARITHMS
Indices
For any real number a ( (, and n is a positive integer, so
[pic] , n times
is call as ‘ a the power of n’, which a is the base and n is the index or exponent.
For example: [pic] [pic]
Law of Indices
a) [pic]
b) [pic]
c) [pic]
d) [pic]
e) [pic]
Zero Index [pic] [pic]
Negative Index [pic]
Fractional Index [pic]
Example:
| | |
|1. [pic] |4. [pic] |
|[pic] |5. [pic] |
|2. [pic] |6. [pic] |
|[pic] |8. [pic] |
|3. [pic] | |
|7. [pic] | |
Exercise:
1. Simplify the following expressions.
a) [pic] b) [pic] c) [pic] d) [pic] e) [pic]
2. If [pic], prove that [pic]
3. Solve the following equations.
a) [pic] b) [pic] c) [pic] d) [pic]
Surds
A surd is an irrational number of the form [pic] , where ‘n’ is a positive integer and ‘a’ is a real number which is not a perfect square. For example, [pic] and [pic] are surd but [pic] is not a surd since [pic].
The following

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