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