Question

How to find $\log$ of any number?

Answer 1

Always Remember these three properties of logarithm;

$\log \left(mn\right)=\log m+\log n$

$\log \left(m/n\right)=\log m-\log n$

and $\log \left(m^n\right)=n\log m$

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).

$\log 2=0.301$

$\log 3=0.477$

$\log 5=0.699$

$\log 7=0.845$

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

and the formula is, $\log (a+b)=\log a+b/(2.42\times a)$

This is a main method to find any log value.

For example, $\log \left(737\right)=?$

$\log \left(mn\right)=\log m+\log n$

$=\log \left(737\right)=\log (7.37\times {10}^2)$

$=\log \left(7.37\right)+\log \left({10}^2\right)$ by using

$=\log \left(7.37\right)+2[\log {10}^n=n]$

$=\log (7+0.37)+2$

Now applying the formula;

$=\log \left(7\right)+0.37/(2.42\times 7)+2$

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.