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    Log Base 2 of −1

    Logarithm Calculator
    Log base
    x

    What is log₂(−1)?

    Answer

    log2(−1)
    does not exist

    log2 is the log base 2.

    2 raised to any power is a positive number, so the negative number −1 cannot be reached.

    We look for y with 2y = −1.

    Oxy1

    The curve y = log2 x passes through (1, 0) and (2, 1) and rises: for x > 1 the log is positive, for 0 < x < 1 negative.

    The graph exists only to the right of the y-axis: there is no point at x = −1.

    Log of −1 in different bases
    BaseNotationValue
    eln(−1)does not exist
    10log(−1)does not exist
    2log₂(−1)does not exist

    See Also

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    https://calculat.io/en/number/logarithm/2---1Copy
    <a href="https://calculat.io/en/number/logarithm/2---1">Log Base 2 of −1 (log₂(−1)) - Calculatio</a>Copy
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    Log Base 2 of −1 (log₂(−1)). log₂(−1) does not exist: 2 raised to any power is positive, never −1. What you may have meant is below.
    https://calculat.io/en/number/logarithm/2---1/generated.jpgCopy

    Log base 2 of nearby numbers

    xlog₂ x
    −1does not exist
    0does not exist
    0.125−3
    1/6≈ −2.5850
    0.25−2
    1/3≈ −1.5850
    0.5−1
    Recalculate with different values ↑

    FAQ

    What is log₂(−1)?

    log₂(−1) does not exist

    Does log₂(−1) exist in complex numbers?

    Yes, in complex numbers: the principal value for x < 0 is log₂ x = (ln|x| + iπ) / ln 2, so log₂(−1) = iπ / ln 2 ≈ 4.5324i. Among real numbers it does not exist.

    What does log without a base mean?

    At school and on a calculator, log x without a base is the common log, base 10: log 100 = 2. In Python, math.log(x) is the natural log ln x; in Excel, LN is the natural log and LOG is base 10.

    See Also