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Logarithms
Chapter Six
Logarithms
FOR ONLINE READING ONLY
Mathematics for Secondary Schools
Introduction
Some real life situations such as earthquakes, population growth, and levels of acid
or alkali in liquids are associated with very large or very small numbers. In such
cases, describing such situations becomes difficult. However the concept of logarithm
has made such descriptions easy for an individual to understand the effects of their
occurrences. In this chapter, you will learn to write numbers in standard form and use
laws of logarithms to solve problems. The competencies developed will enable you to
simplify and find solutions to complex expressions, solve problems related to exponential
growth decay, and understand the science of earthquakes and the spread of diseases,
and many other applications.
Think
Describing real life situations such as magnitudes of earthquakes, the
amount of acid and base in liquids, and population growth without the
knowledge of logarithms.
Standard form of numbers When writing numbers in standard form,
When a number is expressed in the form the following must be considered:
n
A×10 , where 1 ≤ A < 10 and n is an 1. For numbers between 0 and 1, move
integer, it is said to be in standard form the decimal point towards right until
a number is between 1 and 10 is
or scientific notation or standard notation. obtained and the exponent of 10 is
For instance, the following numbers are negative.
expressed in standard form: 2. For numbers greater than or equal
(a) 290 2.9 100 2.9 10= = 2 to 10, move the decimal point left
until the value is between 1 and 10,
(b) 29 2.9 10 2.9 10= = 1 resulting in a positive exponent of 10.
(c) 2.9 = 2.9 10´ 0 3. The exponent of 10 is determined
by the number of places the decimal
1 1 point is moved, either to the right or
(d) 0.29 2.9 0.1 2.9 2.9 10
=
0.29 2.9 = 0.1 2.9 = = = − = 1 2.9 10 − 1
10 10 left.
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