How to find the value of log3 without using of log table?

Trial and error. A logarithm is the power to which a base is raised. 10 to the third power is 1000, so the logarithm of 1000 is three.

Log 3 = 10^x

Guess x = 1/2 then 10^(1/2) = 3.16
Guess x = 0.45 then 10^(0.45) = 1.109 so x is between 0.45 and 0.5
Guess x = 0.48 then 10^(0.48) = 3.01995 so x is less than 0.48
Guess x = 0.475 then 10^(0.475) = 2.985 so x is more than 0.475
And so on.