Exponentials and Logarithms

exp(x)

Computes \(e^{x}\).

>>> exp(3)
= 20.08553692318767
>>> exp(ln(3))
= 3

exp2(x)

Computes \(2^{x}\).

>>> exp2(3)
= 8
>>> exp2(ln2(3))
= 3

expm1(x)

Computes \(e^{x} - 1\) in a way that is accurate for small \(x\).

>>> expm1(20)
= 19.08553692318767
>>> expm1(0.01)
= 0.01005016708416806
>>> expm1(ln(3))
= 2

ln(x)

Computes the natural logarithm \(\log_{e}{x}\).

>>> ln(20)
= 2.995732273553991
>>> ln(exp(20))
= 20

ln2(x)

Computes the logarithm base \(2\), \(\log_{2}{x}\). Aliases: log2.

>>> ln2(8)
= 3
>>> log2(exp2(8))
= 8

ln1p(x)

Computes \(\log_{e}(1 + x)\). Aliases: log1p.

>>> ln1p(8)
= 2.19722457733622
>>> log1p(expm1(8))
= 8

log(x)

Computes the logarithm base \(10\), \(\log_{10}{x}\). Aliases: log10.

>>> log(100)
= 2
>>> log10(10^3)
= 3

log1pm(x)

Computes \(\log_{e}(1 + x) - x\).

>>> log1pm(5)
= -3.208240530771945

logabs(x)

Computes \(\log_{e}|x|\).

>>> log1pm(5)
= 1.09861228866811

logn(a, b)

computes \(\log_{b}{a}\)

>>> logn(2, 3)
= 0.6309297535714574