The antilog, also known as the antilogarithm refers to the reverse log or a logarithm’s inverse function. The antilog of a number (y) equals the base (b) raised to the power of y or the exponent. You can use this antilog calculator to make the calculation conveniently for you.
How to use the antilog calculator?
Also known as an inverse log calculator, this online tool can automatically calculate the antilog value for you. Whether you use it to solve the formula or to check your answer, this tool makes it easier for you. Just follow these steps:
- First, input the Logarithm Value then input the Logarithm Base.
- In doing this, the calculator will generate the antilog value automatically.
What is antilog?
An antilog is the inverse function of a logarithm which means that it’s simply an exponentiation. You can calculate the antilog of a number using this formula:
x = logb-1(y) = by
Since the antilog and log are inverse functions of each other, this means that x = by = blogbx, and y = logbx = logb(by ).
How to find antilog?
Since the antilog is simply a reverse log, it’s common with people who make calculations using slide rules or referencing tables of numbers. Nowadays, it’s easier to acquire this value using online tools such as the antilog calculator. Also, antilog is now more commonly known as the “exponent.” To find the antilog of any number, you have to raise the base of the logarithm to the power of the number. Here are steps to follow when finding the antilog manually:
Define the algorithm
A number’s logarithm refers to the power to raise a given base so you can get that number. For instance, you have to raise the number 10 to the power of 2 to get 100. This means that 2 is the base 10 logarithm of 100.
Describe the inverse function
If a given function (f) gets an input (A) and generates an output (B) and there’s a function (f1) which needs an input (B) to generate (A), this means that (f1) is the inverse function of (f). This shows that antilog = inverse log. When looking at the formula, log (b) x = y has an antilog (b) y = x.
Examine the antilog notation
Let’s examine the formula using values: since log(10) 100 = 2, this means that the antilog is (10) 2 = 100 or 102 = 100.
Calculate the antilog
Solve a given problem to get the antilog. If log (2) 32 = 5, what is the antilog (2) 5? 25 = 32, so antilog (2) 5 = 32.
How do you convert log to antilog?
There are two ways to determine the antilog, and it would depend on whether the log form is positive or negative:
Positive log form
If the positive number has a decimal point, separate the whole number (also known as the characteristic) from the decimal value. Then determine the antilog of the decimal value first. After that, determine the antilog of the whole number or the characteristic. To get the final antilog value, multiply the antilog you acquired for the decimal value with the one you acquired for the characteristic. Here’s an example:
- For instance, we want to get the antilog of 3.8734
- Separate the characteristic from the decimal value.
- So you get the values 3 and .8734.
- First, determine the antilog value of .8734. You can get this value by checking the reference table for finding the antilog of decimal values. In this case, the antilog is 7.47.
- After that, determine the antilog of the characteristic which is 103.
- For the last step, multiply the two values you’ve acquired to get the final antilog which is 7470.
- When looking at the formula, 3.8734 = 7.47 X 10^3 = 7470.
Negative log form
When it comes to finding the antilog of a negative log form, things can get quite tricky. This is especially true if the number has a decimal value as well. You may have to perform a lot of calculations to get the final antilog value that you need. Therefore, you would have to take an additional step to convert the negative log form into a positive value. Here is an example complete with the steps for you to follow:
- For instance, we want to get the antilog of -4.5611.
- Since the characteristic of this negative log is 4, you first add the next whole number to it: -4.5611 + 5.
- However, simply adding 5 would modify the original log. Therefore, you need to subtract the same number to it: -4.5611 +5 -5
- In doing this, you will get the value .4399 – 5.
- This log form is equal to the original negative log form but with a positive decimal value. This makes it easier to find the antilog of the said value. Again, use the reference table to find the antilog of the decimal value which, in this case, is 2.75.
- Now you can determine the antilog of the negative whole number which is -5, and this would be 10-5.
- To get the final result, multiply the two values you’ve acquired together giving you 2.75 X 10-5.
An example of inverse log calculation
As long as you know a number’s logarithm, you will be able to find its initial value by calculating the antilog. Let’s take a look at an example:
For instance, you want to calculate the algorithm of 3.5. Since this number falls between the numbers 3 and 4, the antilog would result in a value between numbers 1,000 and 10,000. Since antilog and log are inverse functions of each other, this means that
10Log x = x, and Log 10x = x
Antilog or log functions operate on values which are unit less. You can use this formula to solve for the antilog value which is 33.115. But for an easier result which is more accurate, you can use the online antilog calculator.