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    Log of −1 (Base 10)

    Logarithm Calculator
    Log base
    x

    What is log(−1)?

    Answer

    log(−1)
    does not exist

    log here is the common log, base 10.

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

    We look for y with 10y = −1.

    Oxy

    The curve y = log x passes through (1, 0) and (10, 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

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    https://calculat.io/en/number/logarithm/10---1Copy
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    Log of −1 (Base 10). log(−1) does not exist: 10 raised to any power is positive, never −1. What you may have meant is below.
    https://calculat.io/en/number/logarithm/10---1/generated.jpgCopy

    Common log of nearby numbers

    xlog x
    −2does not exist
    −1does not exist
    0does not exist
    0.01−2
    0.05≈ −1.3010
    0.1−1
    0.3≈ −0.5229
    Recalculate with different values ↑

    FAQ

    What is log(−1)?

    log(−1) does not exist

    Does log(−1) exist in complex numbers?

    Yes, in complex numbers: the principal value for x < 0 is log x = (ln|x| + iπ) / ln 10, so log(−1) = iπ / ln 10 ≈ 1.3644i. Among real numbers it does not exist.

    What is e?

    e ≈ 2.71828 is the base of the natural logarithm: ln x is the logarithm of x to base e, so ln e = 1. It is an irrational number, like π.

    See Also