Log Calculator

Solve logb(x) = y for whichever of base, argument, or result you don't already know.

What a logarithm answers

logb(x) = y asks: "what power do I need to raise b to, to get x?" It's the inverse of exponentiation — where an exponent tells you what a repeated multiplication produces, a logarithm tells you how many multiplications it took to get there.

The three common bases

Base 10 (written just "log") is common in science and engineering. Base e (written "ln", the natural logarithm) shows up throughout calculus and physics. Base 2 (the binary logarithm) is standard in computer science. This calculator accepts any positive base, including "e" typed directly.

Logarithms are only defined for positive arguments, and the base must be positive and not equal to 1 — logb(0) is undefined, and the log of a negative number requires complex numbers.

Common questions

Why is logb(b) always 1?

Because raising b to the power 1 gives you b back — by definition, that's exactly what the logarithm is asking.

How do I convert between log bases?

Use the change-of-base rule: logb(x) = logk(x) / logk(b) for any base k. This is exactly how this calculator computes logs in any base internally, using natural log (ln) as the common base k.

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