Log Calculator with Any Base

This tool calculates the Logarithm with base b of a number x.

Formula

y = Log_b(x)

Background

The Logarithm base b = 4 of x = 64 is 3.

What is a Logarithm?

A logarithm answers the question: “To what power must the base be raised to produce a given number?” Mathematically, the logarithm of a number x with base b is expressed as:

log⁡_b(x) = y

where

b^y = x

Here, b is the base, x is the number, and y is the logarithm result.

For example:

• Log⁡₂(8) = 3 because 2³ = 8
• Log⁡₁₀(100) = 2 because 10²=100

How to Use the Tool

1. Input the Base and Number: Enter the desired base (b) and the number (x) for which you want to calculate the logarithm.
2. The tool will instantly compute log_⁡b(x)
3. Examples
   • Input: Base = 5, Number = 125
   • Output: Log⁡₅(125)=3