Table of Contents

Last modified on May 25th, 2024

Antilogarithm (in short, antilog) is the inverse operation of the logarithm. The logarithm takes a number and returns the exponent to which the base is raised to obtain that number, while the antilogarithm takes an exponent and raises the base to it.

Mathematically, **if log**_{b}**x = y, then b**^{y}** = x and antilog**_{b}**(y) = x**

For example, as the logarithm (base 10) of 100 is 2, the antilogarithm of 2 is antilog(2) = 100.

While computing the natural log’s antilogarithm, we raise ‘e’ to that power. For example, if ln1 = 0, then e^{0} = 1, and thus, the antilogarithm (base e) of 0 is antilog_{e}(0) = 1.

We can use the antilog of a number easily using a scientific calculator. However, if we are not provided a calculator, we can find the antilogarithm values of a positive or a negative number using the antilog table given below.

The antilog table is divided into three blocks:

- The
**first block**is the main column (the first column) with numbers from 0.00 to 0.99 - The
**second block**(the differences columns) with digits 0 to 9 - The
**third block**(the mean differences columns) with digits 1 to 9

Now, using the antilog table, let us find the antilogarithm value (base 10) of the number 2.3924.

**Step 1: **Separating the characteristic part (the integer part) and the mantissa part (the decimal part), we get:

Characteristic part = 2 and mantissa part = 0.3924

**Step 2: **Now, let us find the corresponding value of the mantissa part 0.3924 from the antilog table.

The corresponding difference value in row number 2, which starts with 0.39, is 2466.

**Step 3: **The corresponding mean difference value in row number 4, starting with 0.39, is 2.

**Step 4: **Adding the obtained values, we get 2466 + 2 = 2468

**Step 5: **The decimal point is placed in the position obtained by adding 1 to the characteristic part. Here, on adding 1 to the characteristic part 2, we get 1 + 2 = 3

Thus, by adding the decimal point after 3 digits from the left, we get 246.8

Thus, the antilog of 2.3924 is 246.8

Now, let us find the antilog of 2.3924

Here, the characteristic part = 2, and the mantissa part = 0.3924

Thus, antilog(2.3924) = 10^{2} × 10^{0.3924}

Since, 10^{0.3924} ≈ 2.468

⇒ antilog(2.3924) = 100 × 2.468

⇒ antilog(2.3924) = 246.8

**Find antilog(1.7845) using the antilog table.**

Solution:

Here, the characteristic part = 1 and the mantissa part = 0.7845

The corresponding difference value of the mantissa part in row number 0.78 and starting with 4 is 6081

The corresponding mean difference value in row number 5, starting with 0.78, is 7

Now, on adding the obtained values, we get 6081 + 7 = 6088

Since the characteristic part is 1, the decimal point is placed after 2 (= 1 + 1) places from the left.

By adding the decimal point, we get 60.88

Thus, antilog(1.7845) = 60.88

**Find antilog(3.0103)**

Solution:

Here, antilog(3.0103) = 10^{3} × 10^{0.0103}

Since 10^{0.0103} ≈ 1.024

⇒ antilog(3.0103) = 1000 × 1.024

⇒ antilog(3.0103) = 1024

Thus, antilog(3.0103) = 1024

Last modified on May 25th, 2024