Natural Log of 40

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What is ln 40?

Answer

ln 40 ≈
3.6889

ln is the natural log, base e ≈ 2.71828.

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

ln 40 is the power you raise e ≈ 2.71828 to, to get 40: ey = 40.

e³ ≈ 20.0855 < 40 < e⁴ ≈ 54.5982, so 3 < ln 40 < 4

Oxy

Answer point ≈ (40, 3.6889).

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 40 in different bases
BaseNotationValue
eln 40≈ 3.6889
10log 40≈ 1.6021
2log₂ 40≈ 5.3219

See Also

Recalculate with different values ↑

Natural log of nearby numbers

xln x
20≈ 2.9957
21≈ 3.0445
30≈ 3.4012
40≈ 3.6889
42≈ 3.7377
50≈ 3.9120
60≈ 4.0943

FAQ

What is ln 40?

ln 40 ≈ 3.6889

What is the difference between ln 40 and log 40?

ln 40 is the logarithm to base e, log 40 is to base 10: ln 40 ≈ 3.6889, log 40 ≈ 1.6021. One is the other divided by ln 10: log 40 = ln 40 / ln 10 ≈ 1.6021.

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