Question

How to read log & anti log table??????

Answer 1

f x is a positive real number then log x can be written aslog x =  characteristic of x  +  mantissa of x.Remember that the base is 10 and we are considering natural logarithms or logs only.Characteristic of x is an integer that can be either positive or negative depending on whether x > 1 or 
0 < x <1.Mantissa of x has to be read from the log tables.i) How to determine the characteristic of a logx :If x > 1,  then count the digits on the left of the decimal point; if the number of digits is y,  then the characteristic is (y - 1).If 0 < x < 1, then count the number of zeroes appearing in the right side of the decimal point; if the number of zeros is z, then the characteristic is ñ ( z + 1 ).  This is 
                         _____
also written as ( z + 1 ), read as (z + 1 ) bar.ii)       How to determine the mantissa of a logx :As mentioned earlier, the mantissa has to be read from a standard log table.  Log tables consist of rows that go from 10,11, up to 99.  The columns have values 0,1, 2, up to 9. Beyond the 10 columns, there is another column which is known as the mean difference. For determining the mantissa, a particular row has to be read off and the mean difference has to be added from the table.
2. AntilogarithmAntilogarithm is the exact opposite of logarithm of a number.If x = log b, then antilog (x) = b = . 
Remember that antiloga (x) =  .Antilog table for base 10 is readily available. Antilog tables are used for determining the inverse value of the mantissa. From the characteristic, the position of the decimal point can be determined.Antilog tables consist of rows that go from .00, . 01, up to .99.  The columns have values 0,1, 2, up to 9. Beyond the 10 columns, there is another column which is known as the mean difference. For determining the antilog of the numbers after the decimal point,  a particular row has to be read off and the mean difference has to be added from the table.Example 1 : 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.