1. Logarithm:
3. Common Logarithms:
Logarithms to the base 10 are known as common logarithms.
The logarithm of a number contains two parts, namely 'characteristic' and 'mantissa'.
Characteristic: The internal part of the logarithm of a number is called itscharacteristic.
Mantissa:
If a is
a positive real number, other than 1 and a^{m} = x,
then we write:
m = log_{a}x and we say that the value of log x to the base a is m.
2. Properties of Logarithms:
m = log_{a}x and we say that the value of log x to the base a is m.
2. Properties of Logarithms:
3. Common Logarithms:
Logarithms to the base 10 are known as common logarithms.
The logarithm of a number contains two parts, namely 'characteristic' and 'mantissa'.
Characteristic: The internal part of the logarithm of a number is called itscharacteristic.
Case I: When the
number is greater than 1.
In this case, the
characteristic is one less than the number of digits in the left of the decimal
point in the given number.
Case II: When the
number is less than 1.
In this case, the
characteristic is one more than the number of zeros between the decimal point
and the first significant digit of the number and it is negative.
Instead of 1, 2
etc. we write 1 (one bar), 2 (two bar), etc.
Examples:
Number

Characteristic

Number

Characteristic

654.24

2

0.6453

1

26.649

1

0.06134

2

8.3547

0

0.00123

3

Mantissa:
The decimal part of
the logarithm of a number is known is its mantissa. For
mantissa, we look through log table.
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