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Algebra

Logarithm Calculator

The logarithm logₐ(x) answers the question: to what power must the base a be raised to get x? This calculator uses the change-of-base formula logₐ(x) = ln(x)/ln(a) and verifies the answer by raising the base back to that power.

Logarithm Calculator

Logarithm of a value in any base, via change of base.

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Frequently asked questions

What is the change-of-base formula?

Any logarithm can be rewritten with natural logs: logₐ(x) = ln(x) / ln(a).

What bases are allowed?

Any positive base other than 1, and any positive value. Logarithms of zero or negative numbers are undefined for real results.

Can the result be negative?

Yes. When the value is between 0 and 1 the logarithm is negative.

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