Log Calculator (Any Base)
log_b(x) is the power you raise b to in order to get x; for example log₂(64) = 6 because 2⁶ = 64. Use the log_b key for any base, ln for base e and log for base 10.
At a glance
| What it is | Free log calculator: find log base 10, natural log ln, log base 2 or any base. Learn the change-of-base rule. Answers update as you type. |
|---|---|
| Type | Interactive guide with a calculator |
| Level | High school and college |
| Price | Free, with no account or sign-up |
| Works offline | Yes, after the first visit; installs as an app |
| Made by | Aalok (aalok.builds@gmail.com) |
| Last updated | 1 November 2026 |
Key facts
| Definition | log_b(x) = y means bʸ = x |
|---|---|
| Change of base | log_b(x) = ln(x) ÷ ln(b) |
| Special values | log_b(1) = 0 and log_b(b) = 1 |
| Product / quotient | log(xy) = log x + log y; log(x/y) = log x − log y |
| Domain | x > 0 |
Common examples
log₁₀(1000) = 3, ln(e²) = 2, log₂(1024) = 10 and log₅(125) = 3.
How to use it in Plotline
- log₂(64) is already entered; its answer shows next to the input.
- Use log_b for any base, ln for base e and log for base 10.
- Press = to keep the answer in the history, then use ans in the next calculation.
Frequently asked questions
What is log base 2 of 8?
3, because 2³ = 8. Type the base and the number into the log key and the answer appears as you type. The same pattern works for any base: log base 5 of 125 is 3, because 5³ = 125.
What is the difference between log and ln?
log normally means log base 10, and ln means log base e, where e ≈ 2.718. Both answer the same question — what power the base is raised to — so log(1000) = 3 and ln(e) = 1.
Is it free?
Yes. The scientific calculator is free with no account and no sign-up, and every function is available: logs, roots, trigonometry, factorials, powers and constants. It installs as an app on a phone or computer and works offline.
Learn more
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Plotline is an independent project and is not affiliated with Desmos, Texas Instruments or Casio.