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    Log Base 2 of 0

    Logarithm Calculator
    Log base
    x

    What is log₂ 0?

    Answer

    log2 0
    does not exist

    log2 is the log base 2.

    2 raised to any power is greater than zero, so no power gives 0. The closer x gets to 0, the lower log2 x: log₂ 0.001 ≈ −9.9658.

    We look for y with 2y = 0.

    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 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

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    https://calculat.io/en/number/logarithm/2--0Copy
    <a href="https://calculat.io/en/number/logarithm/2--0">Log Base 2 of 0 (log₂ 0) - Calculatio</a>Copy
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    Log Base 2 of 0 (log₂ 0). log₂ 0 does not exist: 2 raised to any power is positive, never 0. What you may have meant is below.
    https://calculat.io/en/number/logarithm/2--0/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 0?

    log₂ 0 does not exist

    What does log₂ x approach as x approaches 0?

    It decreases without bound (to −∞): log₂ 0.001 ≈ −9.9658, log₂ 0.0001 ≈ −13.2877. 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