# MTH5P1:Surds, Indices, and Logarithms

##### This unit is about Surds, Indices and Logarithms for Advanced student level.

For all real x, y > 0 , and all integers a > 0 , A number which can be expressed as a fraction of integers (assuming the denominator is never 0)

is called a rational number. Examples of rational numbers are 5/2, -4/5 and 2.

A number which cannot be expressed as a fraction of two integers is called an irrational number.

Examples of irrational numbers are A number which can be expressed as a fraction of integers (assuming the denominator is never 0) is called a rational number. Examples of rational numbers are 5/2, -4/5 and 2.

An irrational number involving a root is called a surd. Surds occur frequently in trigonometry,
calculus and coordinate geometry. Usually, the exact value of a surd cannot be determined but an
approximate value of it can be found by using calculators or mathematical tables. In this chapter, General Rules of Surds
Multiplication of surds Division of surds

These rules are useful for simplifying two or more surds of for combining them into one single
surd.  Rationalization of the Denominator.

When a fraction has a surd in its denominator, e.g. it is usual to eliminate the surd in the denominator. In fact, the writing of surds in the denominators of fractions should be avoided.
The process of removing this surd is called rationalizing of the denominator. are specially related surds known as conjugate surds. The product of conjugate surds is always a rational number. For example Example 3 Example 4

Solution:

Simplify Example 5

Simplify, without using tables or calculators, the value of ## Indices

If a positive integer a is multiplied by itself three times, we get means the nth power of a, where n is any positive index of the positive integer a.

Rules of Indices
There are several important rules to remember when dealing with indices.
If a, b, m and n are positive integers, then   Solving Exponential Equations
Example 3
Solve the following exponential equations   Example 5  Logarithms
Definition:  Laws of Logarithms Changing the Base of Logarithms  Laws of Logarithms  Changing the Base of Logarithms ## STEM Elearning

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