BYTETOOLS

Logarithm Calculator

Calculate the logarithm of a number with any base, including log base 10, natural log (ln) and log base 2. See the result and an inverse check, all in your browser.

2
log base 10 of 100

Result & inverse check

log10(100) = 2

Check: 10 ^ 2 = 100

What is the Logarithm Calculator?

The ByteTools Logarithm Calculator finds the logarithm of a number to any base. Presets cover the three most common: base 10 (common log), base e (natural log, ln) and base 2, and you can type any custom base you need.

  • Logarithm to base 10, e (natural log) or 2
  • Custom base support for any positive base
  • Inverse check confirms the result
  • Handles decimals and very large or small inputs
  • Guards against non-positive numbers and invalid bases
  • 100% private — runs entirely in your browser

How to use the Logarithm Calculator

  1. 1

    Enter the number you want the logarithm of.

  2. 2

    Choose a base preset — 10, e or 2 — or type a custom base.

  3. 3

    Read the logarithm result.

  4. 4

    Check the inverse verification that base raised to the result returns your number.

  5. 5

    Click Copy to grab the result.

About the Logarithm Calculator

The ByteTools Logarithm Calculator finds the logarithm of a number to any base. Presets cover the three most common: base 10 (common log), base e (natural log, ln) and base 2, and you can type any custom base you need. The result comes with an inverse check that confirms it is correct.

It is built for maths and science students, engineers and anyone working with exponential growth, decibels, pH or information theory. Seeing the inverse (raising the base back to the result) makes the answer easy to trust.

All calculation happens locally in your browser with JavaScript. Nothing is uploaded, so the tool is private, instant and works offline. Copy the result with one click.

Frequently asked questions

What is a logarithm?

A logarithm answers the question: to what power must the base be raised to get this number? Since 10² = 100, the log base 10 of 100 is 2. Logarithms are the inverse of exponentiation.

What is the difference between log and ln?

The notation log usually means base 10 (the common logarithm), while ln means base e, where e ≈ 2.71828 (the natural logarithm). Both measure the same idea with a different base. This calculator provides presets for each.

How do you calculate a logarithm with any base?

Use the change-of-base formula: log_b(x) = ln(x) ÷ ln(b), or equivalently with log base 10. The calculator applies this so you can enter any positive base other than 1 and get an accurate result.

Why can't you take the log of zero or a negative number?

No power of a positive base gives zero or a negative result, so the logarithm of zero or a negative number is undefined in real arithmetic. The calculator flags these inputs instead of returning an error value.

What is log base 2 used for?

Log base 2 counts how many times you can halve a number, so it appears in computer science, information theory and algorithm analysis. For example log₂(8) = 3 because 2³ = 8. It is one of the built-in presets.

Guides for Logarithm Calculator

Related tools