Logarithm Calculator

Calculate a logarithm using any positive base other than 1

Your result will appear here.

About the Logarithm Calculator

Logarithms reverse exponentiation: instead of asking for the result of a power, they ask which exponent produces a given value. This calculator handles common, natural and other supported logarithm bases.

The base matters. Common logarithms use base 10, natural logarithms use base e and other bases can be chosen when the problem requires them.

How to Use the Logarithm Calculator

  1. Enter the positive value whose logarithm you want.
  2. Choose the logarithm base or select natural/common log.
  3. Calculate the result.
  4. Check the domain: real logarithms require a positive argument and a positive base other than 1.

How the Calculation Works

The statement log_b(x)=y means b^y=x. The calculator solves for y.

When changing bases, log_b(x)=ln(x)÷ln(b), which allows a logarithm in one base to be computed from another supported logarithm.

Worked example

Logarithm Calculator Worked Example

log₁₀(1,000)

10³ = 1,000, so log₁₀(1,000)=3. Likewise, log₂(8)=3 because 2³=8.

Result guide

Understanding Your Logarithm Calculator Result

A logarithm measures exponent scale. Equal steps in logarithmic value represent multiplicative changes in the original quantity. Logarithmic scales are useful when values span many orders of magnitude because multiplication in the original quantity becomes addition on the logarithmic scale.

Before you rely on the answer

Assumptions and Limitations

  • The logarithm argument is positive in real-number mode.
  • The base is positive and not equal to 1.
  • Displayed decimal results may be rounded.

Practical tip

Using This Result in Practice

When solving exponential equations, rewrite both sides with the same base when possible. If that is not convenient, take logarithms and solve for the exponent. Always write the base when it is not obvious; log₂, log₁₀ and ln can produce very different numerical answers for the same input.

Related calculations

Useful Calculations to Continue With

If you already know the exponent and want to evaluate the power, use the Exponent Calculator.

For very large or small powers of ten used mainly for number formatting, use the Scientific Notation Calculator.

Common questions

Logarithm Calculator FAQ

What is ln?

ln is the natural logarithm, using Euler’s number e as the base.

Can I take log of a negative number?

Not as a real logarithm. Negative arguments require complex-number mathematics.

Why is log base 1 invalid?

1 raised to any real power remains 1, so it cannot produce the range of positive values needed for a logarithm inverse.