Logarithm Calculator — How to Calculate Logs
Calculate log₁₀, ln, or log_b(x) for x > 0. Custom bases use change of base ln(x)/ln(b). Example: log₁₀(1000) = 3. States domain limits (x > 0, b > 0, b ≠ 1). Browser learning tool.
How it works
Choose log₁₀, ln, or a custom base. Enter x > 0 (and base b when custom). The page returns the log via Math.log / Math.log10 with change-of-base for custom bases.
Formula and domains
log_b(x) is the exponent that sends b to x. On this page:
- log₁₀(x) uses common log; ln(x) uses natural log (base e).
- Custom: log_b(x) = ln(x) / ln(b) with b > 0, b ≠ 1, x > 0.
- x must be positive; zero and negatives are rejected.
- Pair with the exponent page to check b^y ≈ x.
Example
Example: log₁₀(1000) = 3.
When to use it
- Homework: evaluate log₁₀, ln, or log₂ of a positive number.
- Check change-of-base arithmetic by hand.
- Prepare exponents for scientific-notation scale checks.
Frequently asked questions
Why must x be positive?
Real logarithms are undefined at 0 and negative numbers on this page.
How is a custom base computed?
Via change of base: ln(x)/ln(b).
What is ln?
Natural log with base e ≈ 2.71828.
Can base be 1?
No. Log base 1 is undefined.
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Questions or feedback
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