Logarithm and antilogarithm both are interconnected terms. Both terms are inverse of each other. Logarithms are used to manipulate large numbers to avoid complicated and complex calculations in many fields of science, technology, mathematics, statistics, engineering, astronomy, etc.

In this article, we will elaborate on the concept of antilogarithm, its basic definition, and methods to compute the antilogarithm. Before introducing antilogarithm, it is mandatory to apprehend the basic concept of logarithm.

**Definition of Antilogarithm:**

The antilogarithm (Antilog) of a number can be defined as If log_{a} x = y then, x = antilog y. It can also be written as **x = log**_{a}^{-1}** y**. The reverse working process to compute the logarithm of a number is known as the antilogarithm of the same number.

Now it is necessary to understand the terms characteristic and mantissa for the computation of antilogarithm. There are two parts of the logarithm of a number, characteristic and mantissa.

**Characteristic:**

The characteristic of the logarithm of a number is defined as the integral part of a number, which is positive for a number > 1 and negative for a number < 1.

Consider **b = a x 10**** ^{n}** where

**1 ≤ a < 10**, the index(power) of 10 is the characteristic of log b. The characteristic of the logarithm of a number > 1 is +ve and it is one less than the number of digits in the integral part of the original number.

On the other hand, the characteristic of the logarithm of a number < 1 is -ve and it is one more than the number of zeros instantly after the decimal point of the number.

**Mantissa:**

The mantissa of the logarithm of a number is defined as the decimal part of a number which is always +ve is known as mantissa of the logarithm of that number.

Logarithm of a number | Characteristic | Mantissa |

log 22.74 = 1.3568 | 1 | .3568 |

log 7859 = 3.8954 | 3 | .8953 |

log 0.0357 = 2.5527 | -2 | .5527 |

**Method to Compute Antilog:**

Here we will discuss two methods to find antilog.

- Using antilog table
- Using calculator

**Using Antilog Table to Compute Antilog:**

- We can observe that an antilog table is split up into three parts.

- Consider only decimal part (mantissa) and ignore characteristic.
- We will observe
**1**^{st}**3**digit of the mantissa will be observed in the second block which is located in yellow color and 4^{rd}^{th}digit of the mantissa will be observed in the third mean difference block which is pointed out with green color. - Observe the row corresponding to
**1**^{st} - Locate the column corresponding to the
**3**digit of the mantissa until it intersects the corresponding located row of 1^{rd}^{st}digits. Note this value. - Now this value will be added with the number at the intersection of this value’s row and the mean difference column corresponding to the
**4**digits of the column.^{th}

Now we will insert the decimal point following the given rules.

- If the characteristic is positive, then its numerical value increases by
**1**and therefore gives the number of figures to the left of the decimal point in the required number. - If the characteristic is negative, then its numerical value will decrease by
**1**and give the number of zeros to the right of the decimal point in the required number.

**Using Calculator to Compute Antilog:**

Using a calculator, it is very convenient to find out antilog. Simply you need to write the logarithmic value of the number as an exponent of **10^**. Applying this you will be able to get the desired answer. e.g. Antilog (2.1645) = 10^^{2.1645}=146.05.

**Example 1:**

Using the antilog table compute the number whose logarithm is 1.0647.

**Solution:**

**Step 1.** Separate characteristic and mantissa part.

characteristic=1, mantissa=.0647

**Step 2.** Locate the row number that starts with .06 and column number 4. You will get the corresponding value of 1159.

**Step 3.** The number at the intersection of this row and the mean difference column corresponding to 7 is 2.

**Step 4.** Sum up these values obtained in step 1 and step 2, we obtain the value 1159 + 2 = 1161

**Step 5.** As the characteristic for this value is 1. Its numerical value increased by 1 (as there should be two digits in an integral part) and therefore inserting a decimal point to the designated place which is fixed after two digits from left in 1161.

Hence antilog (1.0647) = **11.61 **

**Example 2. **

Compute an antilog of 1.0647 using the calculator.

**Solution:**

**Step 1.** Writing this value as an exponent of 10^.

Antilog (1.0647) = 10^^{1.0647} = **11.61 **

**Wrap Up:**

In this article, we elaborated the idea of antilogarithm in detail. We’ve also apprehended the basic definition of logarithm and antilogarithm. Afterward, we’ve explained methods for the computation of antilogarithms.

In the last section, we solved some examples. Hopefully, by understanding this article, we will be able to handle the problems of antilogarithms.