Logarithm II – SS1 Mathematics Lesson Note (First Term)

USING LOGARITHMS TO EVALUATE PROBLEMS OF MULTIPLICATION, DIVISION, POWERS AND ROOTS WITH NUMBERS LESS THAN ONE

OPERATION WITH BAR NOTATION

Note the following when carrying out operations on the logarithm of numbers which are negative.

i.The mantissa (fractional part) is positive, so it has to be added in the usual manner.

ii. The characteristic (integral part) is either positive or negative and should therefore be added or operated as directed numbers.

iii. For operations like multiplication and division, separate the integer from the characteristic before operating.  

Examples:

Simplify the following, leaving the answers in bar notation, where necessary

2. 2.4423 x 3
3. 2.2337 ÷ 7

Solution

2. 2.4423 x 3

= 3(2+ 0.4423)

= 6 + 1. 3269

= 5.3269

2. 2.2337 ÷ 7

= 7 + 5.2337 ÷ 7

= 1 + 0.7477

= 1.7477

ASSIGNMENT 

Evaluate using logarithm.

1. 23.97  x   ✓0.7124

3.877 x 52.18