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The detailed guide below is currently available in English.
What a logarithm asks
A logarithm reverses exponentiation: log_b(x) answers "b raised to what power gives x?" So log₂ 8 = 3 because 2³ = 8, and log₁₀ 1000 = 3 because 10³ = 1000. Any base works via the change-of-base rule log_b(x) = ln(x) ÷ ln(b), which is exactly how this calculator evaluates custom bases. The natural log, written ln, uses the base e ≈ 2.71828 and appears throughout science whenever growth or decay compounds continuously, while base 10 suits everyday magnitudes and base 2 measures information and doubling steps.
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Why can I not take the log of zero or a negative number?
No real power of a positive base ever produces zero or a negative result, so those inputs have no real logarithm. Enter a positive number; complex logarithms exist but are outside everyday use.
How do I enter a natural log?
Choose "e (natural log)" in the base selector, or open the natural-log row in the results — ln(x) is computed for every input regardless of which base you picked.