Evaluate numerically:

Evaluate to high precision:

The precision of the output tracks the precision of the input:

Complex number inputs:

Evaluate efficiently at high precision:

Log2 can deal with real‐valued intervals:

Log2 threads elementwise over lists and matrices:

Values of Log2 at fixed points:

Values at zero:

Values at infinity:

Zero argument gives a symbolic result:

Zero of Log2:

Find a value of x for which the Log2[x]=0.5:

Plot the Log2 function:

Plot the real part of :

Plot the imaginary part of :

Polar plot with :

Log2 is defined for all positive values:

Log2 is defined for all nonzero complex values:

Function range of Log2:

Log2 is not an analytic function:

Nor is it meromorphic:

Log2 has a branch cut along the negative real axis:

Log2 is monotonic on the positive reals:

Log2 is injective:

Log2 is surjective:

Log2 is neither non-negative nor non-positive:

Log2 has both singularities and discontinuities for x≤0:

Log2 is concave on the positive reals:

TraditionalForm formatting:

First derivative:

Higher derivatives:

Plot the higher derivatives:

Formula for the derivative:

Compute the indefinite integral using Integrate:

Definite integral of Log2:

More integrals:

Find the Taylor expansion using Series:

Plots of the first three approximations around :

General term in the series expansion using SeriesCoefficient:

FourierSeries:

Asymptotic expansions at the branch cut:

Log2 can be applied to power series:

Basic identity for Log2:

Logarithm of a power function simplification:

Simplify logarithms with assumptions:

Logarithm of a product:

Change of base:

Expand assuming real variables x and y: