log Logarithm Calculator - log and ln
Calculate logarithm with any base
📌 Info
- logb(x) = ln(x) / ln(b)
- log(10) = 1, log(100) = 2, log(1000) = 3
- ln(e) = 1 (e ≈ 2.71828)
Calculate Logarithms (log, ln, and Any Base)
This logarithm calculator evaluates the common logarithm (base 10), the natural logarithm (ln, base e), and the logarithm of a number to any base you choose. A logarithm answers the question: to what power must the base be raised to produce a given number? For example, the base-10 log of 1000 is 3, because ten raised to the power three equals one thousand.
Logarithms turn multiplication into addition and very large ranges into manageable scales, which is why they appear throughout science and engineering. The natural log is central to calculus, growth and decay problems, and probability, while base-10 logs underpin scales used for sound, acidity, and earthquake magnitude.
How to Use It
Enter the number you want the logarithm of, and choose base 10, base e, or a custom base. The tool returns the result with high precision so you can use it in homework, lab work, or quick checks. For a custom base, the calculator applies the change-of-base relationship, which lets any logarithm be computed from natural or common logs.
Remember that the input must be a positive number, since logarithms of zero or negative values are undefined in real numbers. The calculator is free, runs instantly in your browser, and works on mobile and desktop.