How this calculator works
A logarithm asks which exponent raises a base to the given positive number. Common logarithms use base 10 and natural logarithms use e. For another base, divide the natural log of the number by the natural log of the base. Bases between zero and one are valid, but one itself is not.
Formula
log_b(x) = ln(x)/ln(b), equivalent to b^y = x. Require x > 0, b > 0 and b ≠ 1.
Worked example
log10(1000) = 3 because 10^3 = 1000. ln(10) is about 2.30258509. log2(1024) = 10 because 2^10 = 1024.
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Frequently asked questions
Why is base one invalid?
Every real power of one equals one, so it cannot give a unique exponent for a logarithm.
Can the logarithm be negative?
Yes. For a base greater than one, a positive argument below one has a negative logarithm. For example, log10(0.1) = -1.
How do I enter base e?
Use the natural log mode, which uses e directly. In the chosen-base mode, enter e as a number, about 2.718281828, since the base field is numeric.