Logarithm Calculator
Logarithm in any base plus ln and log₁₀.
Inputs
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Formula
log_b(x) = ln(x) ÷ ln(b)
Logarithms answer 'to what power must base b be raised to get x?' The change-of-base formula converts any log into natural logs, which JavaScript's Math.log computes.
Worked example
log₁₀(100) = 2 because 10² = 100. The same screen shows ln(100) ≈ 4.605 and confirms 10^2 returns 100 via the antilog check row.
Where this can give the wrong answer
- x must be positive — log of zero or a negative number isn't a real number.
- Base must be positive and not equal to 1 — log base 1 is undefined.
- Choosing base e duplicates the natural log row by design — useful for sanity-checking.
FAQ
- ln is log base e (≈ 2.718). Engineers and calculus use ln; decibel and pH-style problems often use log₁₀. This calculator shows both alongside your chosen base.