Natural Log of 21

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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

Recalculate with different values ↑

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

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