original number by knowing its log. While logs are used to represent numbers as powers of a fixed base.

Antilogs reverse this process by determining the number corresponding to a given logic value.

In this article, we will explore the concept of anti-logs in detail; its formula and Calculation; the Properties of

Antilogs; and the Applications of Antilogs. We’ll also some examples for a better understanding of the concept

of Antilog.

Definition of Antilog

The antilog performs the opposite operation of the log. While a log is the exponent to which a particular base

must be raised to produce a given number; the antilog is the opposite operation. It is used to determine the

value that results from raising a specific base to the power of a given number.

Mathematically; the antilog is defined as:

antilog(x) = b x

b represents the log's base in this case.

Properties of antilog:

Antilog possesses several useful properties for mathematical calculations.

1. The log of any base b to the power of 1 is always equal to 1.

2. The antilog of the log of a number is equal to the number itself.

antilog(log(x)) = x log(antilog(x)) = x.

3. The antilog of the sum of two numbers is equal to the product of the antilog of one number and the log

of the antilog of the other number.

antilog (x + y) = x log (antilog (x)) = x.

4. The antilog of the difference in logic values is equal to the quotient of the corresponding antilogs.

(x - y) = antilog (x) / antilog (y).

Performing calculations involving antilogs is simplified with these properties.

Main Components of the Antilog:

Understanding the characteristic and mantissa parts is important before calculating the antilog of a number by

table.

Characteristic: The characteristic refers to every part of a log. Any number bigger than one has a positive log

that is one fewer than the number of digits to the left of the decimal point.

**Steps To Find the Antilog of a Number:**

**antilog**of a given number.

1. Break down the log value into its characteristic and mantissa components.2. Evaluate the antilog of the mantissa part.3. Consider the characteristic: Adjust the decimal location in the antilog determination depending on the characteristic value

Calculation of Antilog:

There are two primary methods for calculating antilog:

** Method 1: **Without Using Table

** Method 2:** Using Logic Tables

**Method 1: Without Using Table**

The formula to find the antilog is:

Antilog(y) = b x

Here;

** x is the log of the number.**

** The base of the log is b**

Let's review the steps for calculating the antilog using the base and log formula:

**Step 1:** Determine the log and its corresponding base.

Consider you have a log x and its base b; such as log b x.

**Step 2: **Take the base b to the power of the log x.

Calculate b x using a calculator or by hand.

**Step 3:** The result of b x is the antilog of “x”.

The obtained value is the antilog of the given log x with the base b.

**Method 2: Using Logic Table:**

An antilog table provides precalculated values of antilogs for a range of logic values; eliminating the need for complex calculations.

**To use an antilog table:**

1. Identify characteristic and mantissa components of the number.

2. Find the corresponding value in the antilog table using the mantissa as the row number and the third

digit of the mantissa as the column number.

3. Observe the mean difference in the matching row linked to the fourth digit of the mantissa.

4. Add the mean difference obtained in Step 3 to the value from Step 2.

5. Place a decimal point immediately after the first digit of the number obtained in step 4.

6. Calculate the product of the number obtained in steps 5 and 10 raised to the power of the

characteristic. The value obtained is the antilog of the original number.

**Uses of Antilog :**

- Antilogs are used to calculate pH levels which measure the acidity or alkalinity of a solution. The pH scale is based on logic principles and antilogs are essential for converting pH readings into numerical values.
- Antilogs are used to analyze stock prices and market trends. Stock prices often exhibit exponential growth or decay patterns, and antilogs can be used to identify these patterns and make predictions about future prices.

**Solved Problems of Antilog:**

**Problem 1:**

**Solution:**

**Step 1:**

Identify the log and its base.

In this case;

y = 8.

b = 2

Take the base 'b' to the power of the log ‘y’.

28 = 256

Step 3:

The result of 28 is the antilog of 8.

The antilog of log28 is 256.

**Problem 2:**

Compute the antilog of 2.1324

**Solution:**

By applying the Antilog table.

Step 1:

Identify the characteristic and mantissa components of the number.

The integer part of the log of the number is two (Characteristics): 2

The number 0.1324 represents the mantissa.

Step 2:

The value is located in row 13 and column 2

Associated value = 1355 + 1 = 1356

Observe the mean difference in the matching row linked to the fourth digit of the mantissa.

= 1355 + 1= 1356.

Since the characteristics are 2 it is increased by 1 (because there should be two digits in an integral part) and therefore the decimal point is fixed after 3 digits.

Step 4:

Place a decimal point immediately after the first digit of the number obtained in step 4.

= 135.6

Hence; the antilog of 2.1324 is 135.6

**Conclusion:**

In this article, we have explored the concept of antilogs in detail, including its formula and calculation, the properties of antilogs, and the applications of antilogs. We also provided some examples to better understand the concept of antilog.

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