Using Log and Antilog in Calculations - SS2 Mathematics Lesson Note

Example 3 Evaluate the following logarithm:

1. \(348.3 \times 5.427\)

\(456.2 \div 98.76\)

\(\frac{{(361.2)}^{3} \times 75.09}{{(11.32)}^{2} \times \sqrt{92.5}}\)

Solution

1. \(348.3 \times 5.427\)

NUMBER	LOGARITHM
\[348.3\]	\[2.5420\]
\[5.427\]	\[0.7346\]
\[348.3 \times 5.427\]	\[2.5420 + 0.7346 = 3.2766\]

\[antilog\ 3.2766 = 1891\]

1. \(456.2 \div 98.76\)

NUMBER	LOGARITHM
\[456.2\]	\[2.6592\]
\[98.76\]	\[1.9946\]
\[348.3 \times 5.427\]	\[2.6592 - 1.9946 = 0.6646\]

\[antilog\ 0.6646 = 4.619\]

1. \(\frac{{(361.2)}^{3} \times 75.09}{{(11.32)}^{2} \times \sqrt{92.5}}\)

NUMBER	LOGARITHM
\[{(361.2)}^{3}\]	\[3 \times 2.5577\]	\[7.6731\]
\[75.09\]		\[1.8756\]
			\[7.6731 + 1.8756 = 9.5487\]
\[{(11.32)}^{2}\]	\[2 \times 1.0539\]	\[2.1078\]
\[\sqrt{92.5}\]	\[1.9661 \div 2\]	\[0.9831\]
			\[2.1078 + 0.9831 = 3.0909\]
				\[9.5487 - 3.0909 = 6.4578\]

\[antilog\ 6.4578 = 2,869,000\]