Evaluate log₁₀(x), ln(x), log₂(x), or log with any positive base b—instant results in your browser, nothing uploaded.
Runs in your browser · No data stored · No signup
A logarithm calculator finds log_b(x)—the power you raise base b to in order to get x. This tool supports log₁₀, natural log (ln), log₂, and any custom positive base, computed locally in your browser.
Uses standard JavaScript Math.log and change-of-base; suitable for education and quick checks—not certified for regulated engineering sign-off.
Logarithms are the inverse of exponentiation. If b^y = x, then log_b(x) = y. The common logarithm uses base 10 (log₁₀), the natural logarithm uses base e (ln), and computer science often uses base 2 (log₂).
For any valid base b (positive, not 1), log_b(x) = ln(x) / ln(b). That change-of-base formula is what this calculator applies—so you can evaluate logs without memorizing tables.
Use logarithms for pH and decibel scales, half-life problems, algorithm complexity (log₂ n), and undoing exponential growth in finance or science. Pair with an exponent calculator when you need b^y instead of solving for y.
log₁₀, ln, log₂, or custom base—positive x only; runs locally, never uploaded.
Type the number whose logarithm you want. Logarithms are only defined for x > 0.
Select common log (base 10), natural log (base e), log base 2, or switch to custom and enter your own base b.
For custom base, b must be positive and cannot be 1 (log₁(x) is undefined). The tool uses ln(x)/ln(b).
The result shows log_b(x) with high precision. Use copy or share when documenting homework or lab work.
Verify by raising b to the result power in the exponent calculator— you should recover x within rounding.
Common real-world scenarios where this tool saves time.
Verify log₁₀, ln, and log₂ answers without a physical scientific calculator.
Evaluate log₂(n) for complexity analysis and binary tree depth estimates.
Convert between log scales (pH, decibels) or apply change-of-base for custom formulas.
Work with continuous compounding and ln-based growth rates alongside exponent tools.
| Log type | Base | Typical use |
|---|---|---|
| Common log (log₁₀) | 10 | pH, decibels, orders of magnitude, log scales on charts |
| Natural log (ln) | e ≈ 2.718 | Calculus, continuous compound growth, physics |
| Log base 2 (log₂) | 2 | Binary bits, algorithm complexity, information theory |
| Custom log_b | Any b > 0, b ≠ 1 | Change-of-base homework, engineering formulas |
| Related tool | Use this tool when | Use related tool when |
|---|---|---|
| Exponent Calculator | You know base and exponent and need b^y (the forward power). | You know x and base and need the exponent y where b^y = x. |
| Scientific Calculator | You only need one or two log evaluations with a full keypad. | You want a focused log tool with presets, custom base, and shareable links. |
Logarithms require x > 0. Use the exponent calculator for negative exponents on positive bases instead.
log₁(x) is undefined because 1^y is always 1. Pick any other positive base.
ln uses base e; log₁₀ uses base 10. They differ—for example ln(10) ≈ 2.303, not 1.
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log_b(x) is the exponent y such that b^y = x. Example: log₁₀(100) = 2 because 10² = 100. Logarithms undo exponentiation.
ln(x) is log with base e (≈2.71828). It appears in calculus, continuous growth, and many science formulas. ln(1) = 0 and ln(e) = 1.
log₂ counts how many times you can halve a number—common in binary search complexity O(log₂ n), information theory, and bit-length estimates.
The exponent calculator computes b^y (forward power). This tool solves for the exponent: given x and b, find y in b^y = x.
No real number y satisfies b^y = negative x when b is positive. Complex logarithms exist but this tool returns real results only.
Use the change-of-base formula: log_b(x) = ln(x) / ln(b), with x > 0, b > 0, and b ≠ 1.
LOG usually means base 10 (common logarithm). LN means base e (natural log). Always check your device labeling.
Values for x and base b are evaluated locally in your browser—they are not uploaded for logarithm calculations.
Uses standard JavaScript Math.log and change-of-base; suitable for education and quick checks—not certified for regulated engineering sign-off.
Educational math tool—verify critical calculations independently.
More free tools for the same workflow.
Calculate powers like a^b, negative exponents, and fractional exponents with clear results and quick examples like 2^3 = 8. Runs locally in your browser when supported—no upload required for normal use.
Calculate square roots, cube roots, and nth roots with decimal precision and simplified radical form for integers. Runs locally in your browser when supported—no upload required for normal use.
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Reviewed by EverydayTools Editorial Team on 2026-05-21.
Keys: 1 log₁₀ · L ln · 2 log₂. x must be positive; custom base b ≠ 1.
Base: log₁₀
log_b(x) is the power you raise b to get x. For homework, use quick starts for log₁₀(100), ln(e), and log₂(8)—nothing is uploaded.