Use of the Antilogarithm table - SS2 Mathematics Lesson Note

If \(\log_{10}100 = 2\), then the antilogarithm of \(2\) to base \(10\) is \(100\). That is, \({antilog}_{10}2 = 100\). Antilogarithm is the reverse of logarithm. It is finding the number whose logarithm is given and is obtained via the antilogarithm table.

Example 2 Find the \(antilog\) of \(0.4771\) and \(2.6992\)

Solution

1. Looking at the mantissa \(4771\): in the \(antilog\) table look up \(47\) under \(7\), add difference from column \(1\): \(2999 + 1 = 3000\)

From the characteristic part of \(0\), we add \(1\)and get \(0 + 1 = 1\). Hence, there is one digit before the decimal point, \(3.000\). so the \(antilog\ 0.4771 = 3.000\)

1. Looking at the mantissa \(6992\): in the \(antilog\) table look up \(69\) under \(9\), add difference from column \(2\): \(5000 + 2 = 5002\)

From the characteristic part of \(2\), we add \(1\)and get \(2 + 1 = 3\). Hence, there is three digit before the decimal point, \(3.000\). so the \(antilog\ 0.4771 = 500.2\)