Log Calculator

You type a number and choose a base, and it returns the logarithm using the change-of-base rule, dividing the natural log of your number by the natural log of the base. It also shows the three logs people use most, base 10, natural, and base 2, at the same time. Everything runs in your browser, so you'll see the result the moment you type, and nothing you enter leaves your device. Tap a base chip to switch quickly.

A logarithm answers the question: what power do I raise the base to in order to get this number? So log base 10 of 100 is 2, because 10 squared is 100. For any base, you can use the change-of-base formula: the log equals the natural log of the number divided by the natural log of the base. That's exactly what this tool does, so it'll handle base 7 or base 1.5 just as easily as the common bases.

They're both logarithms, just with different bases. Log usually means base 10, the common logarithm, written log without a subscript in everyday math. Ln means the natural logarithm, base e, where e is about 2.71828, and it shows up all over calculus and growth problems. There's also log base 2, common in computing. This tool shows all three at once, plus whatever custom base you enter, so you don't have to convert between them.

It lets you find a log in any base using a calculator that only does base 10 or base e. The rule is that log base b of x equals log of x divided by log of b, where those two logs can be in any single base you like, as long as they match. So log base 2 of 8 is ln 8 over ln 2, which is 3. It's the trick behind this tool, and it's why any base works here.

Because you can't raise a positive base to any real power and land on zero or a negative number, so the logarithm of zero or a negative isn't defined in the real numbers. As the number shrinks toward zero the log heads to negative infinity, and at exactly zero there's no answer. The base also has to be positive and not equal to 1, since 1 raised to any power is always 1 and could never reach a different number.

Yes, it's completely free, with no sign-up, and it runs right in your browser, so nothing you enter leaves your device. Type a number, pick or type a base, and read the logarithm with the common, natural, and binary logs beside it. Bookmark it for algebra, calculus, chemistry, or computer science homework, and you'll have the change-of-base formula and the answer together whenever you need them.