Logarithm Calculator
Calculate log base 10, natural log (ln), log base 2, or any custom base. Instant results with a logarithm properties reference.
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Logarithm Type
Properties of Logarithms
logₕ(1) = 0Log of 1 is always 0
logₕ(b) = 1Log of the base equals 1
logₕ(xy) = logₕ(x) + logₕ(y)Product rule
logₕ(x/y) = logₕ(x) - logₕ(y)Quotient rule
logₕ(xⁿ) = n · logₕ(x)Power rule
logₕ(x) = logₔ(x) / logₔ(b)Change of base formula
How to Use the Logarithm Calculator
- Select the logarithm type: log base 10, natural log, log base 2, or custom base.
- Enter the number you want to find the logarithm of.
- If using a custom base, enter the base value.
- Click Calculate to see the result instantly.
What Is a Logarithm?
A logarithm answers the question: to what power must a given base be raised to produce a certain number? For example, log base 10 of 100 equals 2, because 10 raised to the power of 2 equals 100.
Features
- Supports log base 10, natural log, log base 2, and custom bases
- Properties of logarithms quick reference
- Instant client-side computation
- No data stored, no sign-up required
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Disclaimer: This tool is provided as-is for informational and educational purposes only.