Antilog Table

The Antilog, or “Anti- Logarithm” of a number is the inverse technique of finding the logarithm of the same number. i.e., if log x = y then x = antilog (y)

log x = y ⇒ x = antilog (y)

For example:

• log 1000 = 3, antilog (3) = 10³ = 1000
• log 100 = 2, antilog (2) = 10² = 100

When finding an antilogarithm, we use the anti-log table, look up the mantissa and then use the characteristic to fix the decimal point correctly to the answer.

Below is the antilog table for the common logarithm.

Example 10.2.1 – How to Use the Antilog Table:

Each of the following indicial systems is in the form y = 10^x, use the antilogarithm table to find the decimal number y.

(a) 10^0.2318
(b) 10^1.2574
(c) 10^2.2296

Solution

(a) Let y = 10^0.2318

Step – 1: Express the index as the sum of characteristic and mantissa, i.e,

10^0.2318 = 10⁰ + 10^0.2318

Step – 2: Concentrate only on mantissa in this step. Use the first two digits after the decimal point to be the row number, which is 23, run your finger along the row and stop under 1 (the third digit of mantissa)

This gives 1702.

Step – 3: In the same row, look for the mean difference corresponding to the 4^thdigit of mantissa. Add this to the value from Step – 2. Running your finger along row 23 and stopping under difference 8 will give 3.

Add 3 to 1702 = 1705

Step – 4: Put a decimal point right after the first digit (of the number from Step – 3) always.
Then it becomes 1.705

Step – 5: Multiply the number from Step – 4 by 10^{characteristic} and the result itself is the antilog of the given number.

Therefore, \( \scriptsize y = 10^0 \: \times \: 10^{0.2318} \\ \scriptsize = 1 \: \times \: 1.705 \\ \scriptsize = 1.705\)

(b) \( \scriptsize 10^{1.2574} = 10^{1 \:+\: 0.2574} \\ \scriptsize = 10^1 \: \times \: 10^{0.2574} \\ \scriptsize = 10\: \times \: 1.809 \\ \scriptsize = 18.09\)

(c) \( \scriptsize 10^{2.2296} = 10^{2 \:+\: 0.2296} \\ \scriptsize = 10^2 \: \times \: 10^{0.2296} \\ \scriptsize = 100\: \times \: 1.696 \\ \scriptsize = 169.6\)