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Logarithm calculator - compute log base b of any value

A free online logarithm calculator that computes log base b of a value using log_b(x) = ln(x)/ln(b). Works with base 10, base 2, the natural log base e, or any custom base. Enter a positive value and a valid base to get instant, accurate results for math and science.

Enter a value and a base to see the logarithm.

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How it works

What is a logarithm?

A logarithm answers the question: to what power must the base be raised to produce a given value? In other words, log_b(x) is the exponent that turns the base b into x.

Logarithms turn multiplication into addition and exponents into multiplication, which makes them essential in science, engineering, finance, and computing.

How the calculation works

This tool uses the change-of-base formula log_b(x) = ln(x)/ln(b), so it can handle any valid base. The value must be greater than 0, and the base must be greater than 0 and not equal to 1.

Common bases include 10 (common log), 2 (binary log), and e (natural log, about 2.71828).

Frequently asked questions

›What base does the calculator use by default?

You choose the base. Common choices are 10, 2, and e, but any base greater than 0 and not equal to 1 works.

›Why must the value be positive?

Logarithms are only defined for values greater than 0. The logarithm of zero or a negative number does not exist in real numbers.

›Why can't the base be 1?

A base of 1 raised to any power is always 1, so it cannot produce other values, making the logarithm undefined.

›How do I compute a natural log?

Set the base to e (about 2.71828) to get the natural logarithm, ln(x).

›Can I use decimal bases?

Yes. Any positive base other than 1 is allowed, including decimals like 1.5 or 2.5.

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