Logarithm Calculator

Effortlessly calculate logarithms for any base and explore the logarithmic function visually.

Number (x):

x =

Base (b):

b =

Logarithm (log()):

Logarithm Visualization

Understanding Logarithms

The logarithm is the inverse operation to exponentiation. In simple terms, the logarithm of a number 'x' with respect to a base 'b' is the exponent to which 'b' must be raised to produce 'x'. Mathematically, this is represented as:

$$log_b(x) = y \iff b^y = x$$

Here, 'b' is the base, 'x' is the number, and 'y' is the logarithm. For example, log₁₀(100) = 2 because 10² = 100.

This calculator helps you compute logarithms for any positive base (excluding 1) and any positive number. It's a fundamental tool in various fields like mathematics, science, and engineering for simplifying complex calculations and understanding exponential relationships.

Explore different bases and numbers to see how the logarithm changes and visualize the logarithmic function with the interactive graph provided.