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Characteristic = 2.

For mantissa, read from the table a number 5002. From the rows, choose 50, and read off from the number under the column 0. The number given in the log tables is 6990. Now read, in the same row, the mean difference under 2. This number is given as 2.

Mantissa = 6990 + 2  =  6992.

Thus log 500.2  = Characteristic of 500.2   +    Mantissa of 500.2

                        = 2   +   0.6992  

                        = 2.6992.

Find the antilog of 2.6992.

The number before the decimal point is 2, so the decimal point will be after the first 3 digits.

From the antilog table, read off the row for .69 and column of 9; the number given in the table is 5000. The mean difference in the same row and under the column 2 is 2. To get the inverse of mantissa add 5000 + 2 = 5002.

Now place a decimal point after the first 3 digits and you get the number 500.2

Thus antilog 2.6992 = 500.2