Natural Log of 0.2

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What is ln 0.2?

Answer

ln 0.2 ≈
−1.6094

ln is the natural log, base e ≈ 2.71828.

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

ln 0.2 is the power you raise e ≈ 2.71828 to, to get 0.2: ey = 0.2.

e⁻² ≈ 0.1353 < 0.2 < e⁻¹ ≈ 0.3679, so −2 < ln 0.2 < −1

Oxy1

Answer point ≈ (0.2, −1.6094).

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 0.2 in different bases
BaseNotationValue
eln 0.2≈ −1.6094
10log 0.2≈ −0.6990
2log₂ 0.2≈ −2.3219

See Also

Recalculate with different values ↑

Natural log of nearby numbers

xln x
0does not exist
0.01≈ −4.6052
0.1≈ −2.3026
0.2≈ −1.6094
0.4≈ −0.9163
0.5≈ −0.6931
0.9≈ −0.1054

FAQ

What is ln 0.2?

ln 0.2 ≈ −1.6094

What is the difference between ln 0.2 and log 0.2?

ln 0.2 is the logarithm to base e, log 0.2 is to base 10: ln 0.2 ≈ −1.6094, log 0.2 ≈ −0.6990. One is the other divided by ln 10: log 0.2 = ln 0.2 / ln 10 ≈ −0.6990.

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