Logarithm Calculator

How to Calculate Logarithms in Any Base

A logarithm answers the question: "To what power must I raise the base to get this number?" logₐ(x) = y means aʸ = x.

Change of base formula

Most calculators only have log (base 10) and ln (base e). To find any base: logₐ(x) = ln(x) ÷ ln(a)

Step-by-step

1. Enter the value you want the logarithm of (x).
2. Enter the base (a). Common bases: 10 (common log), 2 (binary log), e ≈ 2.718 (natural log).
3. The calculator computes ln(x) ÷ ln(a) automatically.

Worked example

log₁₀(100): Since 10² = 100, the answer is 2. Using the formula: ln(100) ÷ ln(10) ≈ 4.605 ÷ 2.303 ≈ 2.

When to use

Logarithms appear in pH calculations, earthquake magnitude (Richter scale), sound intensity (decibels), compound interest, and algorithm complexity analysis.