Log calculator
Calculator
The calculator needs JavaScript. The tables below give the same numbers for common cases.
How it is worked out
- log_b(x) = ln(x) ÷ ln(b) = 6.907755 ÷ 2.302585 = 3.
- Check: 10^3 = 1,000.
| Inputs | Answer |
|---|---|
| Calculate: log base b of x; x: 1000; Base b: 10 (common log); Custom base: 5 | log base 10 of 1,000 = 3. |
| Calculate: log base b of x; x: 8; Base b: 2; Custom base: 5 | log base 2 of 8 = 3. |
| Calculate: log base b of x; x: 100; Base b: e (natural log, ln); Custom base: 5 | log base e of 100 = 4.60517. |
| Calculate: b to the power y (antilog); x: 3; Base b: 10 (common log); Custom base: 5 | 10^3 = 1,000. |
How to use it
The logarithm log_b(x) is the power to which b must be raised to get x: log₁₀(1000) = 3 because 10³ = 1000. Any base is reached with the change-of-base rule log_b(x) = ln(x) ÷ ln(b).
The antilog mode does the opposite: it computes b^y. Logarithms are only defined for positive x, and the base must be positive and not 1.
Frequently asked questions
What is log base 10 of 1000?
3.
What is the natural logarithm?
The logarithm to base e ≈ 2.71828, written ln.
Why can't I take the log of a negative number?
No real power of a positive base gives a negative result.
Method: standard arithmetic shown step by step; no outside data is used. Checked 2026-11-12.
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General information only. Results are plain arithmetic on the numbers you enter; check anything important (money, health, school work) against your own records or the official source.