Logarithm Calculator
A logarithm answers the question: what power must the base be raised to, to give this number? Enter a number and a base to find it.
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- Works offline after your first visit
- Saves on this device
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How it works
The logarithm of a number in a given base is the exponent that gives the number. Since ten cubed is one thousand, the base-ten logarithm of one thousand is three.
The natural logarithm uses the base e, about 2.718, and shows up in growth and decay problems. A logarithm needs a positive number, so enter one above zero.
Worked example
The logarithm of 1,000 in base 10 is 3, and the natural logarithm is 6.9078.
Questions
What base should I use?
Base ten is common for everyday counting and science scales. Base two is common in computing. Use whichever base your problem names.
Why can the base not be one?
One raised to any power is still one, so no power of one gives any other number.
Can the number be negative?
Not with real results. A logarithm needs a positive number, so enter one above zero.
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