If a = 1 + log x yz, b = 1 + log y zx and c = 1 + log z xy, then show that ab + bc + ca = abc.

a = 1 + log x yz = log x x + log x yz = log x xyz. b = 1 + log y zx = log y y + log y zx = log y xyz. c = 1 + log z xy = log z z + log z xy = log z xyz. Hence, proved that ab + bc + ca = abc.