Logarithm Calculator
Calculate log base 10, natural log (ln), log base 2, and log to any custom base. Shows step-by-step working — useful for chemistry, information theory, and general math.
log10(1000)
3
How to use the logarithm calculator
Enter the value and the logarithm base. Common bases: 10 (log), e (ln ≈ 2.71828), 2 (used in CS for entropy).
Formula & explanation
log_b(x) = ln(x) ÷ ln(b). Defined only for x > 0 and b > 0, b ≠ 1.
Examples
log₁₀(1000) = 3. ln(e) = 1. log₂(8) = 3.
Frequently asked questions
- Why can't base be 1?
- log_1(x) is undefined — 1 to any power is 1, so it can't equal x except when x = 1.
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