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Antilog Calculator – Antilogarithm

Created by Hanna Pamuła, PhD
Reviewed by Bogna Szyk and Jack Bowater
Last updated: Mar 04, 2024


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 unsure 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 of 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\small y = \log_b x

💡 You might be interested in our log calculator and the exponent calculator.

The ratio of logarithms is used in the logarithmic scale – a nonlinear scale used to compare a 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; and
  • 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 yy, you need to raise the logarithm base bb (usually 10, sometimes ee) to the power of yy:

x=logb1(y)=by\small x = \log_b^{-1}(y) = b^y

Since log and antilog are inverse functions, then this means that:

x=by=blogbx, andy=logbx=logb(by)\small \begin{split} x &= b^y = b^{\log_b x}\text{, and}\\[.5em] y &= \log_b x = \log_b (b^y) \end{split}

An example of inverse log calculation

Here is an example of an inverse log calculation:

  1. Decide on the number you want to find the antilogarithm of; let's say it's 3.

  2. Type in 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?

To 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. For this example, we will choose 2.
  3. Raise the base to the number, 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, 10ˣ.

This function is usually found as an alternative to the log function, but if your 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.

What is the value of antilog₁₀ 100?

The value of antilog₁₀(100) is a googol, which is ten thousand sexdecillion, 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.

A googol 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?

To convert a log to an antilog:

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

Is ln an antilog?

The function ln is not an antilog; it is instead the natural logarithm, that is, the logarithm with a base of e, the Euler number (approximately equal to 2.71828).

An antilog is the reverse of a 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 have the property of representing the digits of the number, but not its magnitude. Therefore, they do not change when we multiply the argument of the function logb by a power of the same base, that is, by bn.

Hanna Pamuła, PhD
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Antilog
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