Logarithm calculator
Work out a logarithm to any base — the calculator uses the change-of-base formula, so bases other than 10 and e are no problem.
The logarithm of 64 to base 2 is 6.
Formula
a is the base and b the number. The change-of-base formula lets you find a logarithm to any base through the natural logarithm.
How we got there
The base must be positive and not equal to 1, and the number must be positive. Otherwise the logarithm does not exist.
How to work out a logarithm by hand
- Ask what power the base needs
log₂ 64 asks “2 to what power gives 64”. The answer is 6, because 2⁶ = 64.
- For harder numbers use change of base
log₂ 64 = ln 64 ÷ ln 2. That formula works for any permitted base.
- Check by raising to the power
Raise the base to your answer: 2⁶ = 64. If the original number comes back, the answer is right.
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Frequently asked questions
Six, because 2 raised to the sixth power is 64.
log is base 10 and ln is the natural logarithm to base e ≈ 2.718. This calculator accepts any base.
Because 1 to any power is always 1, so the equation would have no unique solution.
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