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Logarithm Calculator

Enter a number and any base to find log base b of x, with the natural log, log base 10, and log base 2 shown alongside, plus an antilog mode for the inverse.

Mode

The logarithm is only defined for numbers greater than 0. Everything runs in your browser. Nothing is uploaded.

Base
Result
Decimals
log10(100) =
2
The exponent that raises base 10 to 100.
Standard logarithms
Natural logln(x)
4.60517
Log base 10log₁₀(x)
2
Log base 2log₂(x)
6.643856
Found with the change of base rule: ln(100) ÷ ln(10).

Everything is calculated in your browser. Nothing is uploaded.

How to calculate a logarithm online

  1. Choose a mode

    Keep logarithm to find the log of a number, or switch to antilog to raise a base to a power.

  2. Enter your number

    Type the number whose logarithm you want, which must be greater than 0 in logarithm mode.

  3. Pick a base

    Select 10, e, or 2, or enter a custom base such as 5 or 1.5.

  4. Read and copy

    The result and the three standard logarithms update instantly, ready to copy as a plain summary.

Why use this tool

Any base you like

Pick 10, e, or 2 with one tap, or type any positive base, whole or decimal, to get log base b of x.

Three standard logs at once

Every entry also returns the natural log, the base 10 log, and the base 2 log side by side.

Antilog mode

Flip to the inverse to raise a base to a power, with e to the x, 10 to the x, and 2 to the x shown together.

Handles the undefined cases

A number of 0 or below, and a base of 0, negative, or exactly 1, are caught with a clear note instead of a wrong answer.

Scientific notation for extremes

Very large or very small antilog results are written in standard form so nothing shows as a misleading 0 or infinity.

Runs entirely in your browser

Every calculation happens on your device. Nothing you type is uploaded.

About this tool

A logarithm answers a simple question: what power do you raise the base to in order to reach a given number? This calculator finds that power the moment you type. Enter any positive number and pick a base of 10, e, or 2, or type your own, and it returns the result along with the three logarithms you reach for most: the natural log, the base 10 log, and the base 2 log.

It uses the change of base rule, so log base b of x is found from the natural log of x divided by the natural log of b. That means any base works, whole or decimal, not just the common three. Logarithms are only defined for numbers greater than 0, so a zero or negative entry is caught with a short message rather than a broken result, and a base of 0, a negative base, or a base of exactly 1 is flagged as invalid. For raising a base to a power directly, see the exponent calculator.

Switch on antilog mode to run the inverse. Given an exponent x and a base b, it computes b to the power x, alongside e to the x, 10 to the x, and 2 to the x, and writes very large or very small results in scientific notation so nothing overflows to a meaningless value. Choose 2, 4, 6, or 8 decimal places to keep irrational results as short or as exact as you need. For a full keypad of powers, roots, and trig, try the scientific calculator.

Frequently asked questions

How do I calculate a logarithm?
Type your number into the field, choose a base of 10, e, or 2, or enter a custom base, and the result appears instantly along with the natural log, the base 10 log, and the base 2 log. There is no button to press.
How does it work with any base?
It uses the change of base rule: log base b of x equals the natural log of x divided by the natural log of b. Because of this, any positive base other than 1 works, including decimals such as 1.5 or 2.5.
What is an antilogarithm?
The antilog is the inverse of the logarithm. Switch to antilog mode, enter an exponent x and a base b, and it computes b to the power x, along with e to the x, 10 to the x, and 2 to the x.
Why is the log of 0 or a negative number undefined?
No power of a positive base can ever produce 0 or a negative number, so the logarithm of a value at or below 0 does not exist. The calculator flags this instead of returning a false result.
Why can the base not be 1?
Every power of 1 equals 1, so a base of 1 can never reach any other number, which leaves its logarithm undefined. A base of 0 or a negative base is rejected for the same reason.
Is my data uploaded anywhere?
No. Everything runs in your browser; nothing is sent to a server.

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