Logarithm Calculator
Any base, via the change-of-base identity.
Work out Logarithm. Any base, via the change-of-base identity. Handles the cases the shortcuts get wrong.
10 for common logs, 2.71828 for natural.
log₍10₎(1,000)
3
10^3 = 1,000
Every logarithm is a rescaling of every other, so only one needs computing: log_b(x) = ln(x) ÷ ln(b). That change-of-base identity is why a calculator with just ln and log₁₀ can produce any base at all. A logarithm answers "what power gives this number" — here 10 raised to 3 returns 1,000.
How the Logarithm Calculator works
A logarithm answers the question: what power gives this number. Every logarithm is a rescaling of every other, so only one needs computing — log_b(x) = ln(x) ÷ ln(b). That identity is why a calculator with just ln and log₁₀ can produce any base at all.
Also known as: log calculator · natural log calculator · ln calculator · log base 2 calculator
Frequently asked questions
What is a logarithm?
The inverse of exponentiation. log₁₀(1000) = 3 because 10³ = 1000.
What is the difference between log and ln?
Base. 'log' usually means base 10 and 'ln' means base e, about 2.71828. Both are shown here alongside base 2.
What is the change-of-base formula?
log_b(x) = ln(x) ÷ ln(b). It lets any base be computed from natural logs alone, which is exactly what this page does.
Why can't I take the log of a negative number?
Because no real power of a positive base produces a negative result. The logarithm of a negative number exists only in complex numbers.
Put this calculator on your own site
Free to use, on any site, commercial or not. Paste this where you want it to appear. It is a plain iframe, so it works in WordPress, Squarespace, Wix, Webflow, Ghost and anything else that accepts HTML.
<iframe src="https://www.thecalclibrary.com/embed/logarithm-calculator" width="100%" height="640" style="border:1px solid #e2e8f0;border-radius:12px" loading="lazy" title="Logarithm Calculator"></iframe>The only condition is that the credit line stays visible. It sits inside the frame, so you do not have to do anything to keep it.
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