You can simply use use ScalingFunctions
. (It appears red in version 10, but still works.)
function = Log[10, a x + b /. a -> 1];
Plot3D[function, {x, 1, 3}, {b, 1, 3}, PlotLabel -> "Normal"]
Plot3D[function, {x, 1, 3}, {b, 1, 3},
ScalingFunctions -> {Identity, Identity, "Log"}, PlotLabel -> "Log"]