Logarithm Calculator
Logarithms to any base, with the working and the exact answer when there is one.
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How to use this calculator
Enter the base b and the number x. The calculator finds log base b of x, shows the change-of-base working, and gives an exact whole-number answer when x is a power of b.
How it's calculated
log_b(x) = y means b^y = x. Change of base: log_b(x) = ln(x) ÷ ln(b).
Worked example
log base 2 of 8 = 3 because 2³ = 8. log base 10 of 1000 = 3.
Frequently asked questions
Why can't I take the log of a negative number?
No power of a positive base gives a negative result, so the logarithm does not exist.
What is ln?
ln is the natural logarithm, with base e ≈ 2.71828.
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Last updated October 2026. Results are for learning and guidance; always check important work. Calculations run in your browser and are not stored.