# Approximating the Logarithm of Any Base with Continued Fractions

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Continued fractions provide a very effective toolset for approximating functions. Usually the continued fraction expansion of a function approximates the function better than its Taylor or Fourier series. This Demonstration shows the high quality of a continued fraction expansion to approximate the logarithm to an arbitrary real base greater than 1. It uses the Shanks method and is very efficient due to its adaptability for high-speed numerical computer code.

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Contributed by: Andreas Lauschke (March 2011)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

To compute the approximation of the logarithm , two sequences of numbers and are computed as follows:

,

,

...

.

Then

.

## Permanent Citation