# Antilog Calculator (Antilogarithm)

By Hanna Pamuła, PhD candidate
Last updated: Feb 10, 2021

Thanks to the antilog calculator you can calculate the inverse logarithm function. Calculate the antilogarithm of any number with any arbitrary base - whether it is 10, natural antilog or any other number. If you are not sure what the antilogarithm is, read the description below where we explain everything step by step.

## Let's start from the beginning: what is a logarithm?

The logarithm is the inverse function to exponentiation. That means the logarithm of a given number x is the exponent to which the base b must be raised to produce that number x.

y = logbx

The ratio of logarithms is used in logarithmic scale - a nonlinear scale used to compare large range of values. It is widely used in many fields of science:

• Acoustics (check decibel calculator for sound pressure and sound intensity levels)
• Chemistry (for instance pH scale; test our arterial and venous blood pH calculators)
• Probability theory and statistics
• Number theory
• Psychology
• Measuring the earthquake strength

## What is antilogarithm and how to calculate it?

As we said, the logarithm is the inverse function to exponentiation, so... Yes, you're right! The antilogarithm is simply the exponentiation! To calculate an antilog of any number y, you need to raise the logarithm base b (usually 10, sometimes e), to the power of y:

x = logb-1(y) = by

Since log and antilog are inverse functions, then this means that x = by = blogbx, and y = logbx = logb(by ).

## An example of inverse log calculation

1. Decide on the number you want to find the antilogarithm of, let's say it's 3.
2. Type your base - assume we want to calculate the natural antilog. We can enter the approximation of Euler's number which is equal to 2.71828 or just type "e" - the calculator understands it.
3. The antilog value appears below: it's 20.086 (third power of e).

Wasn't that easy with our antilog calculator?

## FAQ

### How do you find the antilog of a number?

1. Decide on the base of your calculation. Regular numbers are base 10.
2. Choose the number you wish to find the antilog of. In our example we will choose 2.
3. Raise the number to the base, bx. In our example the calculation is 102.
4. Marvel at your calculation prowess!

### What are the graphical characteristics of an antilog?

The antilog formula for base 10, y = 10x, will have the following graphical characteristics. As x approaches minus infinity, y will tend towards 0, but never actually touch the x axis. As x approaches infinity, y will also tend towards infinity, but at an exponential pace. The y-intercept is at y = 1. These graphical properties hold true for any positive, non-zero base.

### How do you remove log and antilog?

As log and antilog are inverse functions, you should use one to remove the other. For example, to remove a log, raise both sides of the formula to the base of the log (the antilog). To remove antilog, find the log of both sides with a base equal to the base of the indices.

### How do you do antilog on a calculator?

You will not find an ‘antilog’ button on the calculator, but do not fret, as this is because it is easier to write antilog in its numerical form, 10. This function is usually found as an alternative to the log function, but if you calculator lacks this functionality, you can easily construct it yourself by raising the function to the base of the logarithm, y = bx.

### What is the antilog of 3?

The antilog of 3 will vary depending on the base of the original logarithm. The formula for solving this problem is y = b3, where b is the logarithmic base, and y is the result. For example, if the base is 10 (as is the base for our regular number system), the result is 1000. If the base is 2, the antilog of 3 is 8. If the base is the exponential function (making it the natural logarithm), the result will be 20.09.The antilog of 3 will vary depending on the base of the original logarithm. The formula for solving this problem is y = b3, where b is the logarithmic base, and y is the result. For example, if the base is 10 (as is the base for our regular number system), the result is 1000. If the base is 2, the antilog of 3 is 8. If the base is the exponential function (making it the natural logarithm), the result will be 20.09.

### What is the value of antilog 10 100?

The value of antilog10(100) is a googol, or ten thousand sexdectiollion, 10100, or 1 followed by 100 zeroes. This is found by solving the equation y = bx, where in this instance the base, b, is 10 and x is 100. This is also the number of hypothetical possibilities in a chess game, the number of subatomic particles in the visible universe, and the number of years it would take for a supermassive black hole with roughly the mass of one galaxy to decay.

### How do you convert log to antilog?

1. Note the base of your logarithm.
2. Raise both sides of the equation to that base. This removes the logarithm. E.g., y = log10(9) becomes 10y = 9.
3. Solve the remaining equation.

### Is ln an antilog?

Ln is not an antilog, it is instead the natural logarithm, that is the logarithm with a base of e, the exponential function. An antilog is the reverse of logarithm, found by raising a logarithm to its base. For example, the antilog of y = log10(5) is 10y = 5. The natural logarithm is useful in calculating the amount of time needed to reach a certain level of growth, if, for y = ln(x), y = time and x = value being grown.

### What is a mantissa?

The mantissa, or significand, is the decimal part of a logarithm. For example, in the logarithm 4.2168, the mantissa is 0.2168. Mantissas are used as they represent the digits of the number, but not it magnitude, allowing for quick comparison of results without worrying about how many times the base is present.

While it is easier to use the Omni Antilog calculator, to calculate antilog in Excel:

1. Input your base into a cell (e.g., 10 into cell A1). This step is only necessary if the base varies throughout your data set.
2. In another cell, input the number you wish to find the antilog of (e.g., 2 in cell B1).
3. Calculate the antilog by finding the power of the number to the base. In our example this would be =A1^B1.
4. If the base has not been specified, replace A1 with your desired base.
Hanna Pamuła, PhD candidate
Logarithm value...
with base...
Antilog
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