Logarithm and Natural Log Calculator
Compute log_b(x) for any base, compare natural log (ln), common log (log10), and binary log (log2), and see the function graphed in SVG
Compute the logarithm log_b(x) for any positive base b and argument x, with side-by-side results for the natural log (ln), common log (log base 10), and binary log (log base 2). The logarithmic curve renders live as an SVG graph, so you can see how the function behaves rather than just reading a number.
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How to use
- Enter the base (b) — any number greater than 0 other than 1.
- Enter the argument (x) — any positive real number greater than 0.
- Review the result worked through the change of base formula, plus the graph of the logarithmic curve.
FAQ
- Why can't the base of a logarithm be 1?
- Any power of 1 is still 1, so log base 1 has no solution unless the argument is also 1 — and when it is 1, infinitely many solutions work. Neither case defines a valid function, so base 1 is excluded.
- What happens if I enter zero or a negative number as the argument?
- Over the real numbers, the logarithm is only defined for positive values, so 0 and negative arguments can't be evaluated. They require complex numbers, which this calculator doesn't cover.
- How does the calculator figure out a logarithm for an arbitrary base (b) under the hood?
- Most computing systems don't have a built-in function for logarithms of an arbitrary base, so this calculator relies on the change-of-base formula: log_b(x) = ln(x) ÷ ln(b). In other words, it first computes the natural log (ln) of both the argument and the base, then takes their ratio — a method that produces an accurate result no matter what base you enter.