Antilogarithm Calculator

What is Antilogarithm?

An antilogarithm, also known as an inverse logarithm or exponential function, is the inverse operation to a logarithm. It returns the number whose logarithm (to a specified base) is the given value. In other words, if \(y = \log_b(x)\), then \(x = \text{antilog}_b(y)\) or \(x = b^y\).

How to Calculate Antilogarithm

To calculate the antilogarithm of a number y with base b, we need to find x such that log_b(x) = y. This is equivalent to raising the base b to the power of y. Most scientific calculators have an exponential function (usually labeled as "exp" or "e^x") which can be used for this purpose.

Formula

The general formula for an antilogarithm is:

\[ x = b^y \]

Which is equivalent to:

\[ x = \text{antilog}_b(y) \]

Where b is the base of the logarithm, y is the given logarithm value, and x is the result (the antilogarithm).

Calculation Steps

1. Identify the logarithm value \(y\) for which you want to calculate the antilogarithm
2. Determine the base \(b\) of the logarithm (common bases are 10, \(e\), and 2)
3. Use a calculator or computational tool to evaluate \(b^y\)
4. If using a scientific calculator without a specific base \(b\) exponential function, you can use the property of exponents: \(b^y = e^{y \ln(b)}\)
5. Verify your result by calculating \(\log_b(x)\), which should approximately equal \(y\)

Example

Let's calculate the antilogarithm of 3 with base 2, i.e., \(\text{antilog}_2(3)\):

1. We want to find \(x\) such that \(\log_2(x) = 3\)
2. This is equivalent to calculating \(2^3\)
3. Using a calculator or mental arithmetic, we find that \(2^3 = 8\)
4. To verify: \(\log_2(8) = 3\), which confirms our result

Therefore, \(\text{antilog}_2(3) = 8\)

Visual Representation