Question

Find the value of 19.5 X 0.3 X 12 / 3.6 X5.7 X 0.07 using logarithms.

Answer 1

Basic laws are,
log(ab) = loga+logb
log (a/b) = loga-log b

let x=19.5 X 0.3 X 12 / 3.6 X5.7 X 0.07
taking log on both sides,
log x = log (19.5 X 0.3 X 12 / 3.6 X5.7 X 0.07)
= log 19.5 + log 0.3 +log 12 -log3.6 -log5.7-log0.07
= 1.29-0.52+1.07-0.556-0.755--1.15
= 1.679

Now taking antilog
x = 10^1.679
=47.8

The actual value of the given eqaution is 48.8
If we take more decimel points we get the exact values.