Logarithm Calculator (Log Base b, ln, log10, log2)
Calculate the logarithm of any number in any base (ln, log10, log2 or custom), find an antilog, or solve log_b(x) = y for the base, with the change-of-base steps.
Values are double-precision floating point, shown to 12 significant figures.
| x | log_10 x | ln x | log₁₀ x |
|---|---|---|---|
| 0.001 | -3 | -6.90775527898 | -3 |
| 0.01 | -2 | -4.60517018599 | -2 |
| 0.1 | -1 | -2.30258509299 | -1 |
| 0.5 | -0.301029995664 | -0.69314718056 | -0.301029995664 |
| 1 | 0 | 0 | 0 |
| 2 | 0.301029995664 | 0.69314718056 | 0.301029995664 |
| 5 | 0.698970004336 | 1.60943791243 | 0.698970004336 |
| 10 | 1 | 2.30258509299 | 1 |
| 100 | 2 | 4.60517018599 | 2 |
| 1,000 | 3 | 6.90775527898 | 3 |
A logarithm answers the question "what power gives this number?": log₁₀ 1000 = 3 because 10³ = 1000. This calculator works out logarithms in any base, including the natural log (ln, base e), the common log (base 10) and the binary log (base 2). It also runs the equation the other way: find x from the base and the log (the antilog), or find the base from x and y.
How to use this tool
- Choose what to solve: the logarithm, the antilog (x = bʸ) or the base.
- Pick the base: e, 10, 2, or type any other positive base except 1.
- Enter x and/or y, depending on what you are solving.
- Read the answer to 12 significant figures and the change-of-base working.
Formula
y = log_b(x) ⇔ bʸ = x · log_b(x) = ln x ÷ ln b · b = x^(1/y)
x must be positive, and the base must be positive and not 1. The change-of-base rule lets any logarithm be computed from natural logs. Useful identities: log(xy) = log x + log y, log(x/y) = log x − log y and log(xⁿ) = n log x.
Example
log₁₀ 1000 = 3, since 10³ = 1000. For base 3, log₃ 81 = 4 because 3⁴ = 81; by change of base, ln 81 ÷ ln 3 = 4.394449 ÷ 1.098612 = 4. The natural log of 10 is 2.30258509299, and the antilog 2¹⁰ is 1,024.
Frequently asked questions
What is the difference between log and ln?
ln is the natural logarithm, base e ≈ 2.71828. "log" usually means base 10 in school maths and on calculators, but in many programming languages and higher mathematics log means ln.
Why can't I take the log of a negative number?
No real power of a positive base gives a negative number or zero, so the real logarithm is undefined there. Complex logarithms exist but are outside this calculator.
What is an antilog?
The inverse of a logarithm: the antilog of y in base b is bʸ. The antilog of 2 in base 10 is 100.
Sources
Last updated:
Page address with these inputs: https://kakao.mobile/tools/logarithm-solver/
Cite or embed this tool
kakaoCalc. (2026, November 8). Logarithm Calculator (Log Base b, ln, log10, log2). https://kakao.mobile/tools/logarithm-solver/
“Logarithm Calculator (Log Base b, ln, log10, log2).” kakaoCalc, 8 Nov. 2026, kakao.mobile/tools/logarithm-solver/.
Paste this code into your page. The widget runs in your visitors' browsers, shows no ads and keeps a link back to this page. Embedding terms