Antilog Table

Log to Antilog Table

Assume that you are multiplying a number twice. You do this to find the square root of a number. Again, if the same number is multiplied three times by itself, you would be finding the cube of the number. Now, let’s say you reverse this entire process. What are you finding here? The root of a number. It can be square root or it can be the cube root of the number. This is a Hercules as well as a time-consuming task. Here, you will be learning a new topic called antilogs. Understanding this concept will help you ease your problems. In addition to that, antilogs have a wide range of applications in the field of maths. 


Definition of Antilog

Antilog is the shorter version of Anti-Logarithms. When you find the logarithm of a number, you follow a process, the inverse process is used to find the antilog of a number. Let’s say a is the log of number b with base x. Then we can say that b is antilog of a. 


You might have a question: how to see antilog table? Read the article to understand it better.


For example:

 If logx a = b  

                      

Then, b = antilog a

                      

Then, b = antilog a


How to calculate Antilog

There are two methods using which one can calculate the log to Antilog of a number:


  • Using an antilog table

  • Antilog calculation 


Before we go ahead, here are a few things you need to know about the characteristic and the mantissa parts. 


Let’s consider a number 7.345


Here, 

  • 7 is the characteristic

  • 345 is the mantissa


Characteristics is the whole number while the mantissa is all the numbers after the decimal point.


Method 1: Calculating the antilog using Anti log table

Follow the steps given below to calculate the antilog of a number using the antilog table.


Let us consider a number: 2.5463


Step 1: The first thing to do is to separate the characteristic and the mantissa part. In the above example, the characteristic part is 2 while the mantissa part is 5463.


Step 2: Using the antilog table, find the corresponding value of mantissa. Find the row number that is equivalent to .54 nad then choose column number 6. The corresponding value is 3516.


Step 3: Now move to the mean difference column. Again use the .54 row and see what’s the corresponding value under the column 3. In this case, the value is 2.


Step 4: Add the values you found out in step 2 and step 3. Here, it is - 3516 + 2 = 3518


Step 5: In this step, we add the decimal. According to Step 1, we find the characteristic part. Add 1 to the characteristic part. In this case, we found out that the characteristic part is 2. So here, there have to be 3 numbers before the decimal point.


Therefore, the antilog of 2.5463 = 351.8


Method 2: Calculating the antilog 

How to take antilog in a calculator? This might be a question running in your head. Well, it is simple to do that. Follow the steps given below to calculate the antilog of a number using a simple calculator. 


Let us consider a number: 2.5463


Step 1: The first thing to do is to separate the characteristic and the mantissa part. In the above example, the characteristic part is 2 while the mantissa part is 5463.


Step 2: In this method, you’ll have to know the base. Generally for numeric computations, the base is always assumed to be 10. So, to calculate the antilog you need to use the base 10.



Step 3: In this step, you calculate the 10x. Since the base of the number is always assumed to be 10, the calculation of antilog becomes easier. And if the mantissa is 0 and we just have a whole number, the calculation becomes even simpler. So, 10 times to the power of the given number, gives us the antilog. 


Therefore, \[{\mathbf{1}}{{\mathbf{0}}^{{\mathbf{2}}.{\mathbf{5463}}}} = {\text{ }}351.8\]


You can use any method. Both of them will give you the same outcome. 


Antilog Table

The table given below helps you find the antilog of a number. Here’s antilog table pdf 1 to 100.


Examples:


Question 1: Find the antilog of 2.7531


Solution: Given, number = 2.7531


Step 1: The first thing to do is to separate the characteristic and the mantissa part. Here, the characteristic part is 2 while the mantissa part is 7531


Step 2: Using the antilog table, find the corresponding value of mantissa. Find the row number that is equivalent to .75 and then choose the column number. The corresponding value is 5662.


Step 3: Now move to the mean difference column. Again use the .75 row and see what’s the corresponding value under the column 1. In this case, the value is 3.


Step 4: Add the values you found out in step 2 and step 3. Here, it is 5662 + 3 = 5664.


Step 5: In this step, we add the decimal. According to Step 1, we find the characteristic part. Add 1 to the characteristic part. In this case, we found out that the characteristic part is 2. So here, there have to be 3 numbers before the decimal point.


Therefore, the antilog of 2.7351 = 566.4


Question 2: Find the antilog of 1.4265.


Solution: Given, number = 1.4265


Step 1: The first thing to do is to separate the characteristic and the mantissa part. Here, the characteristic part is 1 while the mantissa part is 4265


Step 2: Using the antilog table, find the corresponding value of mantissa. Find the row number that is equivalent to .42 and then choose the column number. The corresponding value is 2667.


Step 3: Now move to the mean difference column. Again use the .42 row and see what’s the corresponding value under the column 5. In this case, the value is 4.


Step 4: Add the values you found out in step 2 and step 3. Here, it is 2667 + 4 = 2671.


Step 5: In this step, we add the decimal. According to Step 1, we find the characteristic part. Add 1 to the characteristic part. In this case, we found out that the characteristic part is 1. So here, there have to be 2 numbers before the decimal point.


Therefore, the antilog of 1.4265 = 26.71


FAQ (Frequently Asked Questions)

1. What is Antilog?

Antilog is the shorter version of Anti-Logarithms. When you find the logarithm of a number, you follow a process, the inverse process is used to find the antilog of a number. Let’s say a is the log of number b with base x. Then we can say that b is antilog of a.


For example:

If logx a = b  

                      

Then, b = antilog a


2. How to find Antilog in a Simple Calculator?

Simply multiply 10 to the power of the number.


Let us consider a number: 2.5463


Step 1: The first thing to do is to separate the characteristic and the mantissa part. In the above example, the characteristic part is 2 while the mantissa part is 5463.


Step 2: In this method, you’ll have to know the base. Generally for numeric computations, the base is always assumed to be 10. So, to calculate the antilog you need to use the base 10.


Step 3: In this step, you calculate the 10x. Since the base of the number is always assumed to be 10, the calculation of antilog becomes easier. And if the mantissa is 0 and we just have a whole number, the calculation becomes even simpler. So, 10 times to the power of the given number, gives us the antilog. 


3. How to Calculate Antilog of Negative Numbers?

Consider a number: -8.053.


Step 1: Break this into two parts. Characteristic and mantissa. Here, the characteristic is 8 and mantissa is .053.


Step 2: Ignore the negative sign and add 1 to the characteristic value, i.e, 8+1=9.


Step 3: Subtract the mantissa from 1. Hence, 1 - 0.053 = 0.947


Step 4: Now multiple 10-9 x antilog(0.947)


Step 5: The answer = 8.851 x 10-9