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Evaluate log10x
Evaluate ln(x)
Evaluate lognx
Evaluate n-th power
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Binary logarithm calculator

- By Dr. Minas E. Lemonis, PhD - Updated: March 3, 2019

This tool evaluates the binary logarithm of a number: \(\log_{2}{x}\). Enter the argument x below.

x =
Result:
\(\log_{2} {x}\) =
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Definitions

General

The binary logarithm of a number x, is a power p so that 2p = x. In modern notation binary logarithm is written as \(\log_{2}{x}\). Any positive real number has a binary logarithm. The binary logarithm of 1 is 0, while the binary logarithm of 0 approaches negative infinity.

The graph of the binary logarithm function is shown in the figure below. It is a monotonic function.

loge-graph

Properties

The derivative of the binary logarithm function is:

\[ \left(\log_{2} x\right)' = \frac{1}{x}\frac{1}{\ln{2}} \approx \frac{1.44270}{x} \]

The integral of the binary logarithm function is given by:

\[ \int \log_{2} x\, \mathrm{d}x = \frac{x\ln{x}-x}{\ln{2}} +C \]

See also
Evaluate log10x
Evaluate ln(x)
Evaluate lognx
Evaluate n-th power
All evaluation tools