How to find antilog of number?

Answer 1

Formula- Antilog of x is equal to 10x

Going along with the following example, 102.6992 = 500.265 --------------------------------------------------------

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 Example 2 : Find the antilog of 1.0913. The number before the decimal point is 1, the number of zeroes after the decimal point is zero. From the antilog table, read off the row for .09 and column of 1; the number given in the table is 1233. The mean difference in the same row and under the column 3 is 1. To get the inverse of mantissa add 1233 + 1 = 1234. Now place a decimal point before the first digit and you get the number 0.1234. 5.Applications

We will now see how logarithms and antilogarithms of numbers are useful for calculations which are complicated or have very large/small numbers. Example 1 : Find 80.92 * 19.45. Let x = 80.92 * 19.45 Use the log function on both the sides. log x = log (80.92 * 19.45) log (80.92 * 19.45) = log 80.92 + log 19.45 ( from the laws of logarithms) From the log tables we get log 80.92 = 1.9080, log 19.45 = 1.2889 Thus log (80.92 * 19.45) = 1.9080 + 1.2889 = 3.1969 log x = 3.1969 Now use antilog functions on both the sides. x = antilog 3.196 From the antilog tables we see that the antilog of 3.1969 is 1573.0. Example 2 : Find (0.00541 * 4.39)

71.35 Let x = (0.00541 * 4.39)

71.35 Take log functions on both the sides. log x = log ( (0.00541 * 4.39) ) ñ log (71.25) ( from the laws of logarithms) First term on the RHS : log ( (0.00541 * 4.39) ) = log (0.00541 * 4.39 )‡ = 1/2 log (0.00541) + 1/2 log (4.39) log (0.00541) = - 2.2668 ‡ log (0.00541) = - 1.1334 log (4.39) = 0.6423 ‡ log (4.39) = 0.3212 Thus the first term on the RHS : -0.8122 The second term on the RHS : log (71.25) = 1.8527 _

Thus log x = - 2.6649; in terms of bar, this can be written as 3.3351. Now take the antilog functions on both the sides, we get x = 0.002163.