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11 results for “logarithm”

Formulae (11)

\log_b(xy) = \log_b(x) + \log_b(y)

The logarithm of a product equals the sum of logarithms.

\log_b\left(\frac{x}{y}\right) = \log_b(x) - \log_b(y)

The logarithm of a quotient equals the difference of logarithms.

\log_b(x^n) = n \cdot \log_b(x)

The logarithm of a power equals the exponent times the logarithm.

\log_b(x) = \frac{\log_k(x)}{\log_k(b)}

Converts a logarithm from one base to another.

\log_b(xy) = \log_b x + \log_b y

The log of a product is the sum of the logs.

\log_b\frac{x}{y} = \log_b x - \log_b y

The log of a quotient is the difference of the logs.

\log_b(x^n) = n\log_b x

The log of a power brings the exponent to the front.

\log_b x = \frac{\log_k x}{\log_k b}

Convert a logarithm to a different base.

\frac{d}{dx}\ln x = \frac{1}{x}

Derivative of the natural logarithm.

\frac{d}{dx}\ln x = \frac{1}{x}

The derivative of the natural logarithm.

O(\log n)

Runtime that grows logarithmically with input size.