Calculations using Logarithms

The basic principles of calculation using logarithms depend on the laws of indices.

Example 10.3.1 – Multiplication and Division:

Use tables to work out the following:

1. 26.52 × 9.184
2. 912.4  ÷ 94.35

Solution

1^st Method

1. 26.52 × 9.184

Using the tables

i.e \( \scriptsize 10^{1.4235} \: \times \: 10^{0.9630} \)

= \( \scriptsize 10^{1.4235 \:+ \:0.9630} \rightarrow \left(x^a \: \times \: x^b = x^{a \: + \:b} \right) \)

= \( \scriptsize 10^{2.3865}\)

Using the anti-log \( \scriptsize \rightarrow 2.435 \)

Answer = 243.5

2nd Method

2. \( \scriptsize 912.4\: \div \: 53.55 \)

Using the tables

1^st Method

i.e \( \scriptsize 10^{2.9602} \: \div \: 10^{1.7288} \)

= \( \scriptsize 10^{2.9602 \:- \: 1.7288} \rightarrow \left(x^a \: \div \: x^b = x^{a \: – \: b} \right) \)

= \( \scriptsize 10^{1.2314} \) Using the anti-log \( \scriptsize \rightarrow 1.704\)

Answer = 17.04

2nd Method