how to calculate log of a number without using log table

Sometimes, it is necessary to find the log(logarithm) of a number when there is no log table around.
so, the only thing you got is your mind.

below 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. (the mind does n)

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 a formula:

log(a+b)=log a + ( b / (2.42*a) )

main method();

for example consider a small value:

log 737=?

=>log (737) = log (7.37 * 10^2)

=>log (7.37 ) + log (10^2)     [ log mn = log m + log n]

=>log (7.37) +2                     [ log 10^n = n]

=>log(7 + 0.37) + 2

now apply the formula:

=>log(7)+ 0.37/2.42*7 + 2

it comes out to be 2.867

which the log value for 737.

now this technique can be applied to any number.

Thank you,

hope it helps.