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Hitherto only a base 5 BBP-type formula is known for $\sqrt 5\log\phi$, where\mbox{$\phi=(\sqrt 5+1)/2$}, the golden ratio, ( i.e. Formula 83 of the April2013 edition of Bailey's Compendium of \mbox{BBP-type} formulas). In this paperwe derive a new binary BBP-type formula for this constant. The formula isobtained as a particular case of a BBP-type formula for a family of logarithms.

A New Binary BBP-type Formula for $\sqrt 5\,\log\phi$