log_b(x) answers: "to what power must b be raised to get x?" E.g. log₁₀(100) = 2, because 10² = 100.

What is the difference between log and ln?

log (or log₁₀) is the base-10 logarithm. ln is the natural logarithm with base e ≈ 2.71828. ln is used in growth and compound interest calculations.

What is the change of base formula?

log_b(x) = ln(x) / ln(b) = log(x) / log(b). This lets you calculate any base logarithm using any other.

What is an antilogarithm?

The antilogarithm is the inverse of the logarithm. 10^x is the antilog of log₁₀, e^x is the antilog of ln.

📐 Logarithm Calculator

Calculate logarithms or antilogarithms with your chosen base. Presets for log₁₀, ln (natural log) and log₂. You can also enter a custom base.

Change of base: log_b(x) = ln(x) / ln(b)

Base

Value (x)

Result

Formula

log_10(100) = ln(100) / ln(10) = 2

The logarithm calculator works out a logarithm in any base — common log₁₀, natural log ln, log₂ or a custom base. It also computes the antilogarithm and shows the change of base formula, so you understand how the result is formed.

How the calculator works and what it’s for▾

What a logarithm means

A logarithm answers the question: to what power must the base be raised to produce a given number. For example log₁₀(1000) is 3, because 10 to the third power is 1000.

The natural log ln uses Euler's number e as its base, and log₂ is central in computing, where numbers are stored as bits.

The change of base formula

When a base is not directly available, the change of base formula lets you express any logarithm as the ratio of two familiar logarithms, for example by dividing natural logs.

The calculator displays this conversion so you can see the reasoning rather than just the final value.