Natural Log of 3

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Log base
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What is ln 3?

Answer

ln 3 ≈
1.0986

ln is the natural log, base e ≈ 2.71828.

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

ln 3 is the power you raise e ≈ 2.71828 to, to get 3: ey = 3.

e¹ ≈ 2.7183 < 3 < e² ≈ 7.3891, so 1 < ln 3 < 2

Oxy1

Answer point ≈ (3, 1.0986).

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 3 in different bases
BaseNotationValue
eln 3≈ 1.0986
10log 3≈ 0.4771
2log₂ 3≈ 1.5850

See Also

Recalculate with different values ↑

Natural log of nearby numbers

xln x
1.5≈ 0.4055
2≈ 0.6931
e1
3≈ 1.0986
4≈ 1.3863
5≈ 1.6094
6≈ 1.7918

FAQ

What is ln 3?

ln 3 ≈ 1.0986

What is the difference between ln 3 and log 3?

ln 3 is the logarithm to base e, log 3 is to base 10: ln 3 ≈ 1.0986, log 3 ≈ 0.4771. One is the other divided by ln 10: log 3 = ln 3 / ln 10 ≈ 0.4771.

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