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    Log Base 2 of 1/3

    Logarithm Calculator
    Log base
    x

    What is log₂(1/3)?

    Answer

    log2(1/3) ≈
    −1.5850

    log2 is the log base 2.

    ≈ — the logarithm is irrational; the value is rounded to 4 decimal places.

    log2(1/3) is the power you raise 2 to, to get 1/3: 2y = 1/3.

    2⁻² = 1/4 < 1/3 < 1/2 = 2⁻¹, so −2 < log2(1/3) < −1

    log2(1/3) = ln(1/3) / ln 2 ≈ −1.098612 / 0.693147 ≈ −1.5850

    Oxy1

    Answer point ≈ (1/3, −1.5850).

    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.

    Log of 1/3 in different bases
    BaseNotationValue
    eln(1/3)≈ −1.0986
    10log(1/3)≈ −0.4771
    2log₂(1/3)≈ −1.5850

    See Also

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    https://calculat.io/en/number/logarithm/2--1-3Copy
    <a href="https://calculat.io/en/number/logarithm/2--1-3">Log Base 2 of 1/3 (log₂(1/3)) - Calculatio</a>Copy
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    Log Base 2 of 1/3 (log₂(1/3)). log₂(1/3) ≈ −1.5850: the power you raise 2 to, to get 1/3. With the check and the graph.
    https://calculat.io/en/number/logarithm/2--1-3/generated.jpgCopy

    Log base 2 of nearby numbers

    xlog₂ x
    0.125−3
    1/6≈ −2.5850
    0.25−2
    1/3≈ −1.5850
    0.5−1
    10
    21
    Recalculate with different values ↑

    FAQ

    What is log₂(1/3)?

    log₂(1/3) ≈ −1.5850

    How to calculate log₂(1/3) on a calculator?

    Divide the natural logs: log₂(1/3) = ln(1/3) / ln 2 ≈ −1.098612 / 0.693147 ≈ −1.5850.

    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