Question

A lecture on taking log and antilog of any number

Answer 1

How to calculcal log value of any number -

You can know the approximate figures without using calculators.
You just have to remember logarithmic values of some initial prime numbers and some properties of logarithmic functions.

Note: All logs are to the base 10

Values to remember:
log2 = 0.301
log3 = 0.477

Using these, let's calculate some logarithmic values:
log5 = log(10/2) = log10 - log2 = 1-0.301 = 0.699
log7 = (log6 + log8)/2 = (log(2*3) + log(2^3))/2 = (log2 + log3 + 3log2)/2 = 0.8405 (accurate value of log7 = 0.8450)

As seen above, these will not provide quite accurate results, however, it is pretty useful for quick calculations where much accuracy is not required.

Hope this helps.

How to take the Antilog -

Consider your number and its parts.For whatever number you are observing, the characteristic is the part that comes before the decimal point; the mantissa is the part that comes after the decimal point.

• As an example, say you need to find the antilog for 2.6452. The characteristic is 2, and the mantissa is 6452.

Know the base. The mathematical log operator has a parameter known as the base. For numerical computations, the base is always 10. Know, therefore, that when you use this method for calculating an antilog, you will always use a base of 10.

Calculate the 10^x. By definition, the antilog of any given number x is the base^x. Recall that the base for your antilog is always 10; x is the number with which you are working. If the mantissa of the number is 0 (in other words, if the number under observation is a whole number, with no decimal point), the computation is easy: simply multiply 10 times 10 that number of times. If the number is not an even whole, use a computer or calculate to compute 10^x.

• In the example above, we do not have a whole number. The antilog is 10^2.6452, which, using a calculator, comes to 441.7.