I'm not sure what a 20*log10 scale is, but if it is only a special tick distribution for a log10 scale, you can use QwtPlot::setAxisScale or more explicit: QwtPlot::setAxisScaleDiv.

Otherwise you have to implement your own type of QwtScaleEngine.
This sounds more difficult as it is, when you use the implementation of QwtLog10ScaleEngine as starting point.

Uwe