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Logarithm Calculator

Log to any base, natural log and antilog, with the change of base shown.

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Logarithm

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Antilogarithm

The inverse: raise the base to your number.

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A logarithm asks: what power do I raise the base to, to get this number? So log₁₀(1000) is 3, because 10³ = 1000.

Quick Tool Overview

The Logarithm Calculator works out the log of any number to any base, with base 10 and the natural log to base e one click away. Every answer is shown alongside its exponential form, because that pairing is the whole idea of a logarithm.

What it does
Calculates logarithms to any base, plus antilogs
You give it
A number and a base
You get back
The logarithm, its exponential form and the change of base working
Best for
Algebra, pH and decibels, growth rates and computer science
Calculators Free, unlimited use No sign-up Runs in your browser

About the Logarithm Calculator

Work out the logarithm of any number to any base, with log base 10 and the natural log to base e available in one click. Every answer is shown alongside its exponential form, so log base 2 of 32 = 5 is presented next to 2 to the power of 5 = 32.

That pairing is the whole idea of a logarithm: it answers the question "what power do I raise this base to in order to get that number?" Because most calculators only offer base 10 and base e, the change of base formula is shown for any other base, which is also how this tool computes it. There is an antilog panel for going the other way, and a note on the domain, since the log of zero or a negative number does not exist.

Key features of the Logarithm Calculator

Any base, not just 10 and e

Log base 2 or base 7 are computed directly, where most calculators force you to convert first.

Exponential form shown

Log base 2 of 32 = 5 is presented next to 2 to the power of 5 = 32, which is what makes logs click.

Change of base formula displayed

The formula is shown rather than hidden, because it is also how the tool computes an arbitrary base.

Antilog panel

Go the other way and recover the number from its logarithm.

Domain explained

The log of zero or a negative number does not exist, and the calculator says why instead of returning an error code.

How to use the Logarithm Calculator

  1. 1

    Enter the number

    Type the value you want the logarithm of. It must be greater than zero.

  2. 2

    Set the base

    Use the shortcuts for base 10 and base e, or type any other base such as 2.

  3. 3

    Check the exponential form

    The equivalent power statement is shown with the answer so you can sanity-check it.

Frequently asked questions

By convention log means base 10 and ln means the natural log to base e, roughly 2.71828. Both answer the same kind of question, they just use a different base.

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