You first have to install the [LevelScheme package](http://scidraw.nd.edu/levelscheme/), it's worth it if you produce a lot of figures.

Load the package:

    << LevelScheme`

Assign a function and do the 3D plot:

    function = Log[10, a x + b /. a -> 1];
    Plot3D[function, {x, 1, 3}, {b, -1, 3}, 
     PlotRange -> {{1, 3}, {-1, 3}, {-1, 1}}, 
     Ticks -> {LogTicks[10, 1, 3], LogTicks[10, -1, 3], LogTicks[10, -1, 1]}
    ]

This would produce this figure:

![enter image description here][1]


  [1]: https://i.sstatic.net/EgQFO.png

`LevelScheme` (and more specifically the [Custom Ticks package](http://library.wolfram.com/infocenter/Demos/5599/)) is really nice to do these things!