Natural Log of 0.4

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What is ln 0.4?

Answer

ln 0.4 ≈
−0.9163

ln is the natural log, base e ≈ 2.71828.

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

ln 0.4 is the power you raise e ≈ 2.71828 to, to get 0.4: ey = 0.4.

e⁻¹ ≈ 0.3679 < 0.4 < e⁰ = 1, so −1 < ln 0.4 < 0

Oxy1

Answer point ≈ (0.4, −0.9163).

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 0.4 in different bases
BaseNotationValue
eln 0.4≈ −0.9163
10log 0.4≈ −0.3979
2log₂ 0.4≈ −1.3219

See Also

Recalculate with different values ↑

Natural log of nearby numbers

xln x
0.01≈ −4.6052
0.1≈ −2.3026
0.2≈ −1.6094
0.4≈ −0.9163
0.5≈ −0.6931
0.9≈ −0.1054
10

FAQ

What is ln 0.4?

ln 0.4 ≈ −0.9163

What is the difference between ln 0.4 and log 0.4?

ln 0.4 is the logarithm to base e, log 0.4 is to base 10: ln 0.4 ≈ −0.9163, log 0.4 ≈ −0.3979. One is the other divided by ln 10: log 0.4 = ln 0.4 / ln 10 ≈ −0.3979.

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