How do I use anti-log tables?

To determine the anti-log value of a given number, let's use 5.4655 as an example. Antilog(5.4655) =?

The first step is to determine the ‘characteristic’ value and mantissa.

For the given number, the characteristic value is 5, and the mantissa is .4655. In the mantissa, look at the first two digits (.46), go to the anti-log table, and look at the .46 row. Note the value from the row, under column 5. (= 2917); also note the mean difference value, under column 5. (= 3). Now add both of them (2917 + 5 = 2922).

Now, let's discuss the placement of the decimal point. By default, we place the decimal point after the first digit. Next, we multiply the value by 10^(the characteristic value).

i.e., in our example, = 2.922 x 10^(5). Therefore, anti-log(5.4655) = 2.922 x 10^(5).

Let's examine a few additional examples to enhance our understanding.

	Characteristic value	Look-up Antilog table	Mean difference	Total value
Anti-log(8.579) =?	= 8; Mantissa = .579	Look up in the .57 row, under col. 9. (= 3793).	Not needed here, since there is no 4th digit in the mantissa.	Place the decimal point => 3.793. Decide the 10 power => 10^(8). Total = 3.793 x 10^(8)
Anti-log(-3.7586) =? First, make the characteristic positive. = -3.7586 + 4 – 4 = -4 + 0.2414.	= -4; Mantissa = .2414	Look up in the .24 row, under col. 1. (= 1742).	Under col. 4 in mean difference (= 2).	= 1742 + 2 = 1744. Place the decimal point => 1.744. Decide the 10 power => 10^(-4) Total = 1.744 x 10^(-4)