Evaluate log₁₀(x), ln(x), log₂(x), or log with any positive base b—instant results in your browser, nothing uploaded.
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.
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.
Concise answers for common searches — definitions, steps, and comparisons.
log₁₀(100) = 2 because 10 raised to the power 2 equals 100.
No. Values you enter are evaluated in your browser with JavaScript math—they are not sent to EverydayTools servers.
log_b(x) = ln(x) ÷ ln(b) for positive x and valid base b (b > 0, b ≠ 1).
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.
No. Numbers you enter are processed locally in your browser. They are not saved on our servers during normal use.
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.
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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.