CalCon has created an Antilog Calculator to calculate the inverse logarithm function. Calculate the antilogarithm of any number with an arbitrary logarithmic base. In the continuation of this text, we will explain the antilogarithm, how to calculate antilogarithm using a calculator, and more.

Antilog is one of the most important math functions, and to correctly calculate and apply antilog, read more about it below. Meanwhile, you can take a look at our Log Calculator, which allows you to calculate the logarithm with any base.

What is Antilog – Antilogarithm?

The logarithm of any number is expressed as an exponent of another fixed number. It represents the inverse function of the exponential function. For instance, the number 8 can be expressed as the product of three numbers, 2 \cdot 2 \cdot 2 . So to get 8, we multiply the number 2 three times so that the log of 8 is equal to the number 3. Here’s how we can express the previous example:

\log_2 (8)=3

The general equation for the logarithm is given below:

y = \log_bx

The inverse function of the logarithm is the opposite process from the log function, i.e., the antilogarithm. In the main function, the process will start from point A and end at point B, but in the opposite case, it begins from B and ends at A. The inverse function of the logarithm is called the Antilog, Inverse Logarithm or Inverse log.

Why do we need log and antilog?

When numbers are written in the billions and trillions, it is relatively complicated to deal with those amounts because of writing and clarity. Logarithm will work for you, whether it’s income, population growth, or long distances. In addition, it can make it easier to understand many long and complicated equations.

The antilog is used to reverse the logarithm function. We use the antilog to return the original number after using the logarithm.

Finding an antilog has application in science and applied statistics where logarithmic scales simplify the presentation of information. Examples include physical and engineering scales such as those for sound intensity, sound frequency, acid corrosion (pH scale), mineral hardness, and star brightness. Perhaps the most famous is the decibel (dB) scale. Other examples include geosciences that measure the strength of storms and hurricanes and the magnitude of earthquakes. The well-known Richter scale is logarithmic.

Scientists and engineers have used logarithmic tables to calculate inverse logarithms. Today, a practical antilogarithm calculator means you no longer have to rely on log tables, as you can use this Antilog Calculator to calculate antilogarithms quickly.

How to calculate the antilog?

We were reminded earlier that the logarithm function is the inverse function of the exponent. So then, when introducing the notion of antilogarithm, which represents the inverse function of the logarithm, we conclude that antilogarithm is essentially the use of exponent.

To calculate the antilog of a log y, it is necessary to raise the base b to the power of y, and the overview equation is given below:

x = \log_b^{-1}(y)=b^y

where x is the resulting antilog.

To calculate the antilog of natural log you need to do the exponential function as e to the power of log.

How to use the Antilog Calculator?

To find the antilog using calculator, with the specified base, follow these steps:

  1. First, enter the number in the calculator for which the antilog is to be calculated.
  2. Then, enter the base to calculate the antilog.
  3. The result will be the antilog.

For example, let’s calculate the antilog of 2 with base 10 using our calculator.

Entered values in calculator are Logarithm = 2 and Base = 10 . Calculator gives the result as Antilog = 100 .

Antilog formula

As we have already mentioned some formulas and terms, we will summarize with an example of computation and share the fundamental relations between logarithms and antilogarithms.

So the logarithm in general form has a notation like:

y = \log_bx

Antilogarithm can be written as:

x = \log_b^{-1}(y)=b^y

For instance, let’s calculate the logarithm of 64 by base 10. Then, using our Log Calculator, the result obtained is 1.81.

If we take our Antilog Calculator now and enter a value of 1.81 with a base of 10, the result obtained will be 64, of course, considering rounding errors.

Antilog table

Before the advent of computers, there were logarithmic and anti-logarithmic tables for calculating math y = \log (x) functions and inverse functions.

The logarithmic and anti-logarithmic table serves people in math and other physical and chemical sciences to quickly find the approximate values of the logarithm and antilogarithm with any base and to facilitate and speed up math calculations.

The antilog table is used when you have a logarithm value with arbitrary base, and you need to find its original amount before the logarithm procedure. Most logarithmic tables are accurate to three to four digits. The book of math logarithmic plates has an average of 30 pages; if you are on the wrong page, your result will be false.

How to use antilog table?

The so-called standard antilogarithm is used to find the antilogarithm from the tables without the calculator. The following steps need to be executed:

  1. The first step is to disassemble the characteristic and mantissa part of the number
  2. The antilog table also includes columns that give a mean difference. For the same row of mantises, the number of columns in the middle difference equals the fourth digit. Read it and write it down.
  3. Add the amount one to the characteristic. This indicates where to place the decimal point. The decimal point is inserted after so many digits go to the left.
  4. Use the antilog table to find the appropriate value for the mantissa. The first two digits work as a row number, and the third digit is equal to the column number. Read it and write it down.
  5. Add the values thus obtained.
  6. Check the result with a CalCon Antilog Calculator.

Example: Calculate the antilog for the 4.6515

Here we need to find an antilog whose logarithm is 4.6515. From the antilog table, the corresponding row 65 and column 1 equals 4477. The column of mean difference for value 5 is 5. By summing these two values, we have 4477 + 5 = 4482. The decimal point is set to 4 (characteristic) + 1 = 5 digits from the left. Thus, the antilog 4.6515 is approximately 44.820,0, while the more precise calculation can be obtained with a calculator and is 44.822,91.

FAQ

Why and where do we use terms log and antilog?

A logarithm is usually used when numbers are too large or too small for easy handling, as often happens in astronomy or integrated circuits. Once compressed, the number can be converted back to its original form using an inverse operator known as an antilog. All calculations can be done using Log or Antilog calculator, for any base.

What is the antilog formula?

The antilogarithm (or inverse logarithm) is calculated by raising the base b to the exponent of the logarithm y:
x = \log_b^{-1}(y)=b^y

How to find the antilog of a negative number?

First, you must convert the negative number into two parts, one negative (characteristic) and the decimal part (Mantissa) into positive values. For instance, let’s take an antilog of -8.5231 by adding +9 and subtracting -9 as follows: -8.5231 +9 - 9 = -9 + (9-8.5231) = -9+ 0.4769 .
Here, characteristic -9 is placed as an exponent of 10, and you can also find the antilog in the antilog table and then do the multiplication of value from the table with 10-9. Meanwhile, we calculated the same base antilog using our Exponent Calculator. The result is 2.9984 \cdot 10^{-9} .

What is a positive characteristic?

The whole or an integral part of a number is a characteristic. The logarithm characteristic of any number greater than 1 is positive and is one less than the number of digits left of the decimal point in a given number. If the number is less than one, the characteristic is negative, and one is greater than the number zero to the right of the decimal point.
For instance, the characteristic of four is 0, then the characteristic of the number 21 is 1, while the characteristic of the 111 is equal to 2. For the 0.1, the characteristic is equal to -1.

What is a Negative Characteristic?

The logarithm with n zeros immediately after the decimal is – (n + 1) + decimal.

What is a Mantissa?

The mantissa is the decimal part of the logarithm number. Mantissa is always a positive value. The negative mantissa needs to be converted into a positive one.

Antilog of 1.5?

The antilog of 1,5 (with the default base 10, since it’s not specified) can be calculated without calculator and the result is 31.62.

How do you find the antilog of a natural log?

To compute the antilog of a natural log (ln), take e to that power.

Antilog of 15.6?

Antilog of 15.6 can only be calculated using calculator, and the result is 3.981.071705.534.969,50.