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 a square root or it can be the cube root of the number. 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, also known as “Anti-Logarithms” of a number, is the opposite way of finding a logarithm of the same number. Consider, if x is the logarithm of the number y with the base b, then we can say that y is the antilog of x to b. It is described as
If log y = x Then, y = antilog x
Both the logarithm and the antilog have their base as 2.7183. If the logarithm and antilogarithm have their base 10, that should be converted to the natural logarithm and antilog by multiplying by 2.303.
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 characteristics 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 Antilog 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 and 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, 102.5463 = 351.8102.5463 = 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 of Antilog
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 column 1. In this case, the value is 3.
-
Step 4: Add the values you found out in steps 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 column 5. In this case, the value is 4.
-
Step 4: Add the values you found out in steps 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