📊 Logarithm Calculator

Free online logarithm calculator. Compute logarithms with any base, natural log (ln), log₂, log₁₀. Shows antilog verification. Pure frontend math tool.

Number

Base

Custom Base ln (natural log) log₁₀ log₂

How to Use

Enter Number and Base
Type the number you want to compute the logarithm of, and choose or enter a base. Supports any positive base except 1.
Select or Enter Base
Quick-select common bases (ln, log₁₀, log₂) or enter a custom base value for specific calculations.
Get Results
The result displays the logarithm value with 10 decimal precision and verifies with antilog calculation.

FAQ

What is a logarithm?

A logarithm answers: 'To what power must the base be raised to get this number?' E.g., log₁₀(100) = 2 because 10² = 100.

What is the natural logarithm (ln)?

ln is the logarithm with base e (≈2.71828). It's widely used in calculus, physics, and compound interest calculations.

Why can't the base be 1 or negative?

Logarithm base must be positive and not equal to 1. Base 1 would always give 1^x = 1, making the function undefined for other values.

What is the relationship between logarithms and exponentials?

They are inverse functions: log_b(x) = y if and only if b^y = x. The antilog feature verifies this relationship.

Where are logarithms used?

Logarithms are used in: earthquake magnitude (Richter), sound intensity (decibels), pH chemistry, computer science (big O notation), and population growth models.