Antilog Table in math is a refrence tool used to reverse logarithmic computation and retrieve the original number from its logarithmic value.
- It typically provides a pre-computed antilogarithm value for various logarithmic inputs, commonly in base 1o or natural logarithm base( e.g ≅ 2.71828)
- Antilog table allows users to find the number corresponding to a given logarithmic value without performing complex exponential calculations, as the result can be directly read from the table.
Before the widespread use of calculators and computers, antilog tables were frequently used alongside log tables to simplify calculations involving exponentiation, enabling quick conversion from logarithm results back to standard numerical values.
Antilog Table is a mathematical reference tool used to calculate the values of Antilogarithms, which are logarithmic inverse operations. The antilog table consist of list of value, each of which corresponds to the algorithm (10 raised ro the power of) of certain decimal vale.
Antilog Table PDF
Click here to download the PDF version of the Antilog table:
Calculation of Antilog
The logarithm of any number can be divided into two parts: the characteristic and the mantissa. These components help us calculate the value of the antilogarithm for any given logarithmic value.
To calculate the antilogarithm (also known as the inverse logarithm) using the characteristic and mantissa, you need to understand the structure of a logarithmic number. A logarithm can be represented as:
Log(x) = Characteristic + Mantissa
Here,
- Log(x) is the logarithm of the number you want to find the antilogarithm for.
- Characteristic is the integer part of the logarithm, and
- Mantissa is the fractional part of the logarithm.
To find the antilogarithm, we need to calculate,
x = 10 Log(x)
Let's consider an example to understand it better.
Example: Find antilog(2.4567).
Solution:
Let's us assume Log(x) = 2.4567, [Where x is the antilog of 2.4567]
Here, Characteristic = 2 (integer part)
Mantissa = 0.4567 (fractional part)
x = 102 × 100.4567 [100.4567 ≈ 3.016]
⇒ x = 100 × 3.016
⇒ x = 301.6
So, the antilog(2.4567) is approximately 301.6.
How to Use the Antilog Table?
Calculating the Antilog using an Antilog table involves breaking down the given logarithm into its characteristic and mantissa parts. Let's walk through the steps to calculate the Antilog of the number 1.4317 using an Antilog table:
Step 1: Given logarithm: 1.4317.
Separate the integral part (characteristic) from the fractional part (mantissa):
- Characteristic: 1
- Mantissa: 0.4317
Step 2: Find the equivalent value of mantissa using the antilog table. Find the row number that equals .43 and then select column number 1 is the matching value.
Step 3: Proceed to the mean difference column. Use the .56 row again and get the appropriate value in column 8. The value in this case is 7.
Step 4: Add the values you discovered in steps 2 and 3. It is 2698 + 7 = 3697 in this case.
Step 5: Insert the decimal point now. The decimal point always goes in the correct position. You must multiply the characteristic value by 1. You now have 3. Then, after 3 digits, add the decimal point to obtain 369.7.
As a result, the antilog value of 2.5678 is 369.7.
Calculate Antilog using a Calculator
Using a calculator to calculate the Antilogarithm is a simple technique. Most scientific calculators contain a specific button for calculating Antilogarithms, which is typically labelled "10x" or "antilog." Thus, you can use the following steps to find antilog with any scientific calculator.
- Step 1: Use a scientific calculator with an "antilog" or "10x" button.
- Step 2: Input the given logarithm.
- Step 3: Calculate the antilog using the "10x" button on the calculator.
Antilog from 1 to 10
The following table represents the value of antilog from 1 to 10.
x | Antilog(x) = 10x |
|---|
| 1 | 10 |
| 2 | 100 |
| 3 | 1,000 |
| 4 | 10,000 |
| 5 | 100,000 |
| 6 | 1,000,000 |
| 7 | 10,000,000 |
| 8 | 100,000,000 |
| 9 | 1,000,000,000 |
| 10 | 10,000,000,000 |
Antilog vs Log Table
Antilog and Log Tables are both valuable reference tables in mathematics, as well as in physics and chemistry. They are used to manually calculate complex calculations involving exponentials and logarithms.
However, there are some key differences between the two tables, and these differences are listed as follows:
| Aspect | Antilog Table | Log Table |
|---|
| Purpose | Helps find the original number from its logarithm (antilog = 10x). | Helps find the logarithm (log10x or lnx) of a given number. |
|---|
| Content | Contains values that are exponentials of the logarithm. Values. | Contains logarithmic values, typically base 10 or base e (natural logarithm). |
|---|
| Usage | Used to reverse a logarithmic operation or perform exponentiation. | Used to perform logarithmic operations or find the result of such operations. |
|---|
| Example | If you have log base 10 of 2 (log10(2)), you can find the antilog, which is 102 = 100. | If you have a numerical value like 100, you can find its logarithm, which is log base 10 of 100, i.e., log10(100) = 2. |
|---|
| Application | Commonly used in calculations involving exponential growth or decay. | Commonly used in mathematics, engineering, and science for various calculations involving orders of magnitude, exponentiation, and more. |
|---|
Read More,
Important Notes on Antilog Table:
- The Antilog Table gives the value of 10x for the mantissa, with columns for different decimal places.
- The Antilog of a number has two parts: Characteristic (Integral Part) and Mantissa ( Decimal Part).
- We can spilt the number into two parts, use the table for decimal part, and the whole number part.
- The table helps simplify calculations by avoiding the direct computation of powers of 10.
Solved Example of Antilog Table
Example 1: Calculate the antilog of 2.7845.
Solution:
Certainly, let's go through the steps to calculate the Antilogarithm for the given logarithm 2.7845 using the method you've provided:
Step 1: Given logarithm: 2.7845.
Separate the integral part (characteristic) from the fractional part (mantissa):
- Characteristic: 2
- Mantissa: 0.7845
Step 2: Find the equivalent value of mantissa using the Antilog table. Look for the row number that corresponds to 0.78 in the Antilog table. Select column number 4. Let's say you find the value 6081 in this row and column.
Step 3: Proceed to the mean difference column. Use the 0.78 row again and get the appropriate value in column 5. Let's say the value in this case is 7.
Step 4: Add the values discovered in steps 2 and 3. Add 6081 and 7: 6081 + 7 = 608.8.
Step 5: Insert the decimal point. You must multiply the characteristic value by 1. You now have 3. Then, after 3 digits, add the decimal point to obtain 608.8.
Result: The Antilogarithm of 2.7845 is approximately 608.8.
Example 2: Use the antilog formula and a calculator to check the answers in Example 1.
Solution:
By Antilog formula, antilog(x) = 10x
Antilog(2.7845) = 102.7845 = 608.8
A calculator is used to verify the answers.
Example 3: Calculate antilog(4.4771).
Solution:
By Antilog formula, antilog(x) = 10x
antilog(4.4771) = 104.4771
antilog(4.4771) ≈ 26645.82
So, Antilog(4.4771) is approximately equal to 26645.82.
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