What is Antilog? Its Definition, Method, and Examples

Category:Mathematics

Before delving into antilogarithms, let us quickly recap logarithms. Logarithms are mathematical functions that measure the exponent to which a given base must be raised to obtain a specific number. The logarithm of 128 to the base 2 is 7since 2 raised to the power of 7equals128. They help simplify complex calculations involving large numbers.

In this article, we will discuss the definition of antilogarithm in-depth and its mathematical representation. We will learn how to determine the antilog of the given number by different methods. After this, we will solve some examples of antilog to understand it better.

What is Antilogarithm?

Antilogarithm is the reverse process of the logarithm. It refers to finding the original number given its logarithm value. The logarithms convert numbers into exponents, while antilog reverses the process by converting exponents back into numbers. In other words, the antilog “undoes” the effect of the logarithm.

The antilogarithm function is denoted as “antilog” or “10^x” for common logarithms (base 10) and “antilog _b ^x” for logarithms with different bases, where “x” represented the logarithmic value.

Some Important Properties of Antilog

Here are some important properties of antilog:

• The Antilog of zero is always equal to one.
• The Antilogarithm of a negative number is always a positive number. For example, the antilog of -3 with base 10 is 0.001.
• The antilog of a product of two numbers is the sum of the antilog of the two numbers.
• The antilog of a quotient of two numbers equals the difference of the antilog of two numbers.

How to determine antilog by using an antilog table?

To determine antilog by using an antilog table, follow these steps:

1. Write separate the characteristic (integral part) and mantissa (fractional part) of the given number.
2. Findthe first two digits of the mantissa after the decimal point in the left column and find the third digit of the mantissa in the top row of the antilog table. Write the value where the first two digits and a third digit intersect.
3. Find the fourth digit of mantissa in the top row of the mean difference, and write the value where the first two digits and fourth digits intersect.
4. Add the value obtained from step number 2 and step 3.
5. The number of decimal move-forward steps (from the left) is determined by adding 1 to the given characteristic.

You can also take assistance from an antilog calculator to find antilogarithm with steps.

Determining antilog without using an antilog table:

Determine the base of the given logarithm. If the base is not given, it is assumed to the base 10. The antilog is found by raising the base to the power of the given logarithmic value.

For example, if you have log₁₀², you would calculate the antilog as follows:

Antilog (2) = 10² = 100

If you have log₂³, you would evaluate the antilog as follows:

Antilog (3) = 2³ = 8

Similarly, if you have log₅^1.25, you would calculate the antilog as 5^1.25 = 7.4767

How antilog helps us in the calculation?

Log and antilog are used to simplify mathematical expressions involving multiplication, division, exponents, and roots.

• Assign any name (x, y, z, or any other) to the given number or expression.
• Take a logarithm on both sides of the equation.
• Use logarithmic properties.

Log(x*y) = log x + log y

Log (x / y) = log x – log y

Log x ⁿ = n log x

• Find the log of each number involved in the expression. Combine the log values obtained from the log table into a single number.
• Taking antilog on both sides of the equation. The analog will be the answer to the given number.

Solved examples of finding the antilog

Here are some examples of finding an Antilog by using an antilog table and without using an Antilog table.

Example 1:

Evaluate the antilog of 2.0125 with the help of the Antilog table.

Solution:

Step 1: Write separate the characteristics and mantissa part of the given value. Where,

Characteristic = 2

Mantissa = .0125

Step 2: Find the first two digits of mantissa (0.1) in the left column of the antilog table. Observe the third digit of the mantissa (2) in the top row of the antilog table.

Here, 5 and .01 intersect at 1.

Step 4: Add the obtained values from steps 2 and step 3 i.e. 1028 + 1 = 1029

Step 5: Decimal shift forward 3steps from the right side. (By adding 1 in a given characteristic i.e. 2+1 = 3).

Hence, the antilogarithm of 2.0125 is 102.9

Example 2:

Find the antilog 4 with base 2, without using the antilog table.

Solution:

Antilog₂⁴ =?

Antilog (4) = 2⁴ = 16

Thus, the antilogarithm of 4, with base 2 is 16. 

Conclusion

In this article, we have read the definition of antilog. We discussed some important properties of antilog. We learned how to calculate antilogarithms using an antilog table and without an antilog table. We debated on how antilog helps us to simplify complicated questions. Some solved examples of antilog covered in this article, would help find antilog.