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We show that the integral $J(t) = (1/\pi^3) \int_0^\pi \int_0^\pi \int_0^\pidx dy dz \log(t - \cos{x} - \cos{y} - \cos{z} + \cos{x}\cos{y}\cos{z})$, can beexpressed in terms of ${_5F_4}$ hypergeometric functions. The integral arisesin the solution by Baxter and Bazhanov of the free-energy of the $sl(n)$ Pottsmodel, which includes the term $J(2)$. Our result immediately gives thelogarithmic 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 hypergeometricfunctions.

An integral arising from the chiral sl(n) Potts model