Antilog: How to find anti Logarithm of Numbers

Antilog: The words “Anti Logarithm of numbers” simply means the opposite of logarithm of numbers which we have discussed here. It is also provided in the four figure table immediately after the table of logarithm of numbers.

The antilog contains number having the corresponding logarithm in the four figure table. When looking for the anti Logarithm of any given number;

(i). Only the Mantissa of a given logarithm will be looked for in the anti Logarithm table.

(ii). After getting the figure, the decimal point should be placed by observing the opposite of the rules for finding the characteristic in logarithm. Always know that the number of digits in the integer/whole part will be one(1) more than that of the characteristic of the logarithm.

Example 1:

Using the table, Find the anti Logarithm of 1.2948
First step: This is to observe and study the number being given to find its anti Logarithm, “1.” is the characteristic while 2948 is the Mantissa. We have been told that it is only the Mantissa that will be looked for in the anti Logarithm table.

Second step: Look for 29 under 4 which is = 1968, difference 8 = 4

Third step: Is to add the both = 1968 + 4 = 1972
The “1972” is the anti Logarithm.

Fourth step: This is to know the exact place to fix the decimal point.
Note that we have being told that the digits in the whole part should be one(1) more than the characteristic of the logarithm itself. Now, Characteristic is “1.” So the decimal point will definitely come immediately after “9” which will give the anti Logarithm of 1.2948 to be 19.72

Example 2:

Find the anti Logarithm of -3.3426
34 under 2 and difference 6 = 2201
The characteristic is -3 which means that we will have “3 zeros” from the left before the first “2” in 2201
Therefore antilog of -3.3426 = 0.002201

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Using the anti Logarithm table, find the anti Logarithm of the following numbers.

Q1: 0.6942

69 under 4 and difference 2 = 4945
The anti Logarithm of 0.6942 = 4.945

Q2: -1.7422

74 under 2 and difference 2 = 5524
Anti Logarithm of -1.7422 = 0.5524

Q3: 2.5429

54 under 2 and difference 9 = 3490
The anti Logarithm of 2.5429 = 349

Q4: 0.0428

04 under 2 and difference 8 = 1104
Anti Logarithm of 0.0428 = 1.104

Q5: -2.0935

09 under 3 and difference 5 = 1240
The anti Logarithm of -2.0935 = 0.0124

Q6: 0.0927

09 under 2 and difference 7 = 1238
Anti Log of 0.0927 = 1.238

Q7: -1.6008

60 under 0 and difference 8 = 3988
The antilog of -1.6008 = 0.3988

Q8: 3.6724

67 under 2 and difference 4 = 4703
Therefore the anti Logarithm of 3.6724 = 4703

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