SS2 First Term Mathematics Lesson Note – Logarithm II

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WEEK 2:                                                                                       

TOPIC:  logarithm 2

Content:

• Logarithm of numbers less than one, involving: Multiplication, Division, Powers and roots.
• Solution of simple logarithmic equations.

Logarithm of numbers less than one

Simple logarithm operations

To find the logarithms of numbers less than 1, (i.e. numbers between 0 and 1), we use negative powers of 10.

For example, 0.08356 = 8.356 ×10^-2 (standard form)

0.08356 = 10^0.9220×10^-2   (from log tables)

=  10^-2+0.9220

So Log0.08356 = -2+0.9220

Characteristics (i.e. power of 10) = -2

Mantissa = 0.9220

∴-2+0.9220=2 ̅.9220

Note: -2 is called bar 2  i.e. 2 ̅

Example 1: Work out the following giving the answers in bar notation

4 ̅.3×5

1 ̅.6043×4

SOLUTION

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