Logarithm Calculator
Calculate logarithms to any base, plus natural (ln), common (log₁₀) and binary (log₂) logarithms.
Your inputs
Results
log base 10 of 1000
3
- Natural log (ln x)
- 6.907755278982
- Common log (log₁₀ x)
- 3
- Binary log (log₂ x)
- 9.965784284662
✓Exact calculation — rounded only for display
What this calculator does
A logarithm answers “to what power must the base be raised to get x?”. Logs turn multiplication into addition and are used across science and finance.
Formula and method
log_b(x) = ln(x) ÷ ln(b)
Worked example
Calculated by this tool with its default inputs:
Inputs
- Number (x): 1000
- Base (b): 10
Results
- log base 10 of 1000: 3
- Natural log (ln x): 6.907755278982
- Common log (log₁₀ x): 3
- Binary log (log₂ x): 9.965784284662
How to read the results
log₁₀(1000) = 3 because 10³ = 1000.
Assumptions and limitations
- x must be positive; the base must be positive and not 1.
Questions
What is ln?
The natural logarithm, with base e ≈ 2.71828.
Methodology and verification
- Result type
- Exact mathematical calculation (rounded only for display)
- Formula version
- 1.0
- Automated verification
- 5 reference and validation test cases, checked against independently computed values. The site cannot be built if any of them fail.
- Editorial review
- Awaiting human editorial review. The explanation was drafted with AI assistance; the formula and examples are verified by the automated tests above.
Privacy
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