  Let $\alpha=(1+\sqrt 5)/2$, the golden ratio, and $\beta=-1/\alpha=(1 - \sqrt
5)/2$. Let $F_n$ and $L_n$ be the Fibonacci and Lucas numbers, defined by
$F_n=(\alpha^n -\beta^n)/\sqrt 5$ and $L_n=\alpha^n + \beta^n$, for all
non-negative integers. We derive base~$\alpha$ expansions of $\log F_n$, $\log
L_n$, $\arctan\dfrac1{F_n}$ and $\arctan\dfrac1{L_n}$ for all positive integers
$n$.
