Class 11

Math

Algebra

Relations and Functions II

How to find $g$ of any number?

Always Remember these three properties of logarithm;

$g(mn)=gm+gn$

$g(m/n)=gm−gn$

and $g(m_{n})=ngm$

Sometimes, When there is no log table around you, the only thing you got is your mind.Here is a method which can be used to calculate the logarithm of a number if there is no log table to use.This is also helpful if the number is too large to be calculated by a calculator.First of all, remember the following basic log values (its no harm to remember these even if you have log table).

$g2=0.301$

$g3=0.477$

$g5=0.699$

$g7=0.845$

these four values can be applied to calculate the log of any number (size does not matter).

and the formula is, $g(a+b)=ga+b/(2.42×a)$

This is a main method to find any log value.

For example, $g(737)=?$

$g(mn)=gm+gn$

$=g(737)=g(7.37×10_{2})$

$=g(7.37)+g(10_{2})$ by using

$=g(7.37)+2[g10_{n}=n]$

$=g(7+0.37)+2$

Now applying the formula;

$=g(7)+0.37/(2.42×7)+2$

it comes out to be 2.867 which is the log value for $737$.** **

now this technique can be applied to find the log of any number.