Natural Log of −5

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Log base
x

What is ln(−5)?

Answer

ln(−5)
does not exist

ln is the natural log, base e ≈ 2.71828.

e raised to any power is a positive number, so the negative number −5 cannot be reached.

We look for y with ey = −5.

Oxy1

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.

The graph exists only to the right of the y-axis: there is no point at x = −5.

Log of −5 in different bases
BaseNotationValue
eln(−5)does not exist
10log(−5)does not exist
2log₂(−5)does not exist

See Also

Recalculate with different values ↑

Natural log of nearby numbers

xln x
−5does not exist
−2does not exist
−1does not exist
0does not exist
0.01≈ −4.6052
0.1≈ −2.3026
0.2≈ −1.6094

FAQ

What is ln(−5)?

ln(−5) does not exist

Does ln(−5) exist in complex numbers?

Yes, in complex numbers: the principal value for x < 0 is ln x = ln|x| + iπ, so ln(−5) = ln 5 + iπ ≈ 1.6094 + 3.1416i. Among real numbers it does not exist.

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