How to do antilog
LOG is a mathematical tool usually it is known as a
compression operator, because it compresses the number. It is mostly used for
the numbers that are too large or too small to handle (e.g. in Astronomy or in
integrated circuits). But once the log operator is applied and the number is
compressed, to convert it back to the original number we need to apply an
inverse operator which is known as antilog.
The log-antilog operators are also used for mathematical
computation, because it naturally makes some of the demanding mathematical
computations like division much simpler computationally.
The mathematical log operator has a parameter known as base
which is used by the operator for its operation. For numerical computations the
base is always taken as 10. In this tutorial we will see step by step method of
how to calculate the antilog (base 10) of a given number.
Method 1:
Step
1: Take the number under observation: For example let’s take the
number 2.6452, whose antilog is to be found.
Step
2: Separate the characteristic and mantissa: The characteristic of the
number is the part before the decimal point (.) which for the given example is
2.On the other hand the mantissa is the part of the number after the decimal
point which is 6452.
Note: The number
is divided into characteristic and mantissa just because the antilog tables are
arranged with respect to both of these parameters.
Step
3: Pick up values from antilog table. For calculating antilog you will
need an antilog table which is easily available and is often given at the end
of mathematics books. Open the
antilog table and look for the row number consisting of first two digits of
mantissa 6452 i.e. row number .64 and look under the column with column number
equal to the third digit of the mantissa i.e.
5. From the antilog table we can see that the number in row .64 and
under column 5 is 4416.
Note: The decimal
point is added before the row number .64 which is composed of the first two
digits of mantissa 6452.
Step
4: Pick up the value from the mean difference columns. There is also another set of columns in
the antilog table called the mean
difference columns. We will also be needing values from these columns. To
pick up the value from these columns we will look in same row as before i.e. .64 but this time column number will be equal
to the fourth digit of mantissa i.e. 2. So from the table we can see that the
value in the row .64 and under column 2 is actually 2.
Step
5: Add the values obtained in previous two steps (step:3 and step:4) i.e.
4416+2 = 4418.
Step
6: Add the decimal point: After performing the last step now we need
to put the decimal point at appropriate place in the value obtained in the last
step. The decimal point is always put after the (characteristic+1) number of digits. As the characteristic is 2
(found in step 2), so decimal point will be put after 2+1 = 3
number of digits in 4418(obtained in last step). So the antilog of 2.6452 will
be 441.8
Method 2:
Step
1: Take the number under observation: For example let’s take the
number 2.6452 one more time, whose antilog is to be found.
Step
2: Calculate the 10^x : By definition the antilog of a given number x
,is the base^x. Where base is 10 and x is 2.6452. If the mantissa of the number
is 0 then we will have just the characteristic which is a whole number let’s
say a. So the antilog will be 10^a which is also equal to multiplying 10 by 10
a times. But if the mantissa is not 0 as in our case 2.6452 we must use
computer or a calculator to compute 10^x.
Since in our example x=2.6452, so the antilog will be simply
10^2.6452 = 441.7 (by calculator).
Tips:
·
Log and anti-log are extensively used in
scientific computations.
·
They also aid in solving numerical computations.
·
Most mathematical operations like multiplication
or division are simple to handle in log, because in log the division is changed
to difference and multiplication is changed to addition. A very useful property
of log numbers.
·
Method to is rather simple in nature then method
1 but it often needs the assistance of a calculator or any other computational
device.
·
The characteristic and mantissa are just the
names of the part before the decimal point and the part after the decimal point
respectively. They have no special significance.
