Use of the Logarithm table - SS2 Mathematics Lesson Note

The (common) logarithm of a number consists of two parts called the characteristic and the mantissa.

1. To calculate characteristic part of a number, subtract one from the number of digits in the whole number (integral) part of the number whose logarithm we intend to find. In the number \(6789.097\), there are 4 digits in the whole number part, so the characteristic part of its logarithm is \(4 - 1 = 3\)

To calculate the mantissa component, first consider the number as \(6789097\) and approximate it to 4 significant figures as \(6789000\). In the logarithm table, look up the row of \(67\) under the \(8\) column which is \(8312\), then add the value under the difference column of \(9\) which is \(6\). That is, \(8312 + 6 = 8318\)

At the point, we combine the characteristic and the mantissa. Therefore, the logarithm of \(6789.097 = 3.8318\)

 

Example 1 Find the logarithm of \(236.9\) and \({(2.45)}^{3}\)

Solution

1. Logarithm of \(236.9\):

1. Characteristic = \(number\ of\ digits\ in\ the\ whole\ number\ part\ –\ 1\)

\[\rightarrow 3 - 1 = 2\]

1. Mantissa = \(23\) under \(6\), add difference \(9\): \(3729 + 17 = 3746\)

\(\log{236.9}\)= \(2.3746\)

1. Logarithm of \({(2.45)}^{3} = \ \log{14.71}\):

1. Characteristic = \(number\ of\ digits\ in\ the\ whole\ number\ part\ –\ 1\)

\[\rightarrow 2 - 1 = 1\]

1. Mantissa = \(14\) under \(7\), add difference \(1\): \(1673 + 3 = 1676\)

\(\log{14.71} = \ 1.1676\)