A New Binary BBP-type Formula for $\sqrt{5}\log \varphi$

Hitherto only a base 5 BBP-type formula is known for $\sqrt{5}\log \varphi$, where \mbox{$\varphi =(\sqrt{5}+1)\mathrm{/}2$}, the golden ratio, ( i.e. Formula 83 of the April 2013 edition of Bailey’s Compendium of \mbox{BBP-type} formulas). In this paper we derive a new binary BBP-type formula for this constant. The formula is obtained as a particular case of a BBP-type formula for a family of logarithms.