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    Natural Log of 21

    Logarithm Calculator
    Log base
    x

    What is ln 21?

    Answer

    ln 21 ≈
    3.0445

    ln is the natural log, base e ≈ 2.71828.

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

    ln 21 is the power you raise e ≈ 2.71828 to, to get 21: ey = 21.

    e³ ≈ 20.0855 < 21 < e⁴ ≈ 54.5982, so 3 < ln 21 < 4

    Oxy

    Answer point ≈ (21, 3.0445).

    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.

    Log of 21 in different bases
    BaseNotationValue
    eln 21≈ 3.0445
    10log 21≈ 1.3222
    2log₂ 21≈ 4.3923

    See Also

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    Natural Log of 21 (ln 21). ln 21 ≈ 3.0445: the power you raise e to, to get 21. With the check and the graph.
    https://calculat.io/en/number/logarithm/e--21/generated.jpgCopy

    Natural log of nearby numbers

    xln x
    16≈ 2.7726
    18≈ 2.8904
    20≈ 2.9957
    21≈ 3.0445
    30≈ 3.4012
    40≈ 3.6889
    42≈ 3.7377
    Recalculate with different values ↑

    FAQ

    What is ln 21?

    ln 21 ≈ 3.0445

    What is the difference between ln 21 and log 21?

    ln 21 is the logarithm to base e, log 21 is to base 10: ln 21 ≈ 3.0445, log 21 ≈ 1.3222. One is the other divided by ln 10: log 21 = ln 21 / ln 10 ≈ 1.3222.

    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