📉 Logarithm Calculator
A logarithm answers "to what power must the base be raised to get this number?" Enter the number and choose a base.
Logarithm
How the Logarithm Calculator works
Logs in any base are found with the change-of-base rule using natural logarithms.
log_b(x) = ln(x) ÷ ln(b)
log₁₀(1000) = 3 because 10³ = 1000
Step-by-step calculation
- 1Enter the number.
- 2Choose the base.
- 3Use change of base: ln(x) ÷ ln(b).
Worked example
log₁₀(1000) = 3, ln(1000) ≈ 6.9078, and log₂(1000) ≈ 9.9658.
Logarithm Calculator examples
| Number | Logarithm |
|---|---|
| 500 | 2.69897 |
| 750 | 2.87506126 |
| 1,000 | 3 |
| 1,250 | 3.09691001 |
| 1,500 | 3.17609126 |
Other inputs kept at the calculator's default values. Results calculated by this calculator.
Why use a Logarithm Calculator?
Solve exponential equations, pH, decibels and more.
Important factors that can affect your results
- Only positive numbers have real logs.
- Base cannot be 1.
- log vs ln notation.
Frequently asked questions
What is ln?
The natural logarithm, with base e ≈ 2.71828.
Can I take the log of 0 or a negative number?
No — logarithms are only defined for positive numbers.
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Last reviewed November 2026 · How we build and check our tools · Report a problem