  We show that the integral $J(t) = (1/\pi^3) \int_0^\pi \int_0^\pi \int_0^\pi
dx dy dz \log(t - \cos{x} - \cos{y} - \cos{z} + \cos{x}\cos{y}\cos{z})$, can be
expressed in terms of ${_5F_4}$ hypergeometric functions. The integral arises
in the solution by Baxter and Bazhanov of the free-energy of the $sl(n)$ Potts
model, which includes the term $J(2)$. Our result immediately gives the
logarithmic Mahler measure of the Laurent polynomial $k - (x+1/x) - (y+1/y) -
(z+1/z) + 1/4(x+1/x) (y+1/y) (z+1/z)$ in terms of the same hypergeometric
functions.
