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    Natural Log of 0

    Logarithm Calculator
    Log base
    x

    What is ln 0?

    Answer

    ln 0
    does not exist

    ln is the natural log, base e ≈ 2.71828.

    e raised to any power is greater than zero, so no power gives 0. The closer x gets to 0, the lower ln x: ln 0.001 ≈ −6.9078.

    We look for y with ey = 0.

    Oxy1

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

    The graph has no point at x = 0: the curve goes down along the y-axis.

    Log of 0 in different bases
    BaseNotationValue
    eln 0does not exist
    10log 0does not exist
    2log₂ 0does not exist

    See Also

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    Natural Log of 0 (ln 0). ln 0 does not exist: e raised to any power is positive, never 0. What you may have meant is below.
    https://calculat.io/en/number/logarithm/e--0/generated.jpgCopy

    Natural log of nearby numbers

    xln x
    −5does not exist
    −2does not exist
    −1does not exist
    0does not exist
    0.01≈ −4.6052
    0.1≈ −2.3026
    0.2≈ −1.6094
    Recalculate with different values ↑

    FAQ

    What is ln 0?

    ln 0 does not exist

    What does ln x approach as x approaches 0?

    It decreases without bound (to −∞): ln 0.001 ≈ −6.9078, ln 0.0001 ≈ −9.2103. There is no value at x = 0 itself.

    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