Create a LogarithmicAxisValueConverter, and set the ChartAxis.ValueConverter of the axis that you want to have the log scale to this converter:

CopyLog scaling the Y axis
<ms:Chart>
<ms:Chart.Resources>
  <ms:LogarithmicAxisValueConverter x:Key="LogScale" Base="10" />
</ms:Chart.Resources>
<ms:Chart.YAxis>
  <ms:ChartAxis ValueConverter="{StaticResource LogScale}" />
</ms:Chart.YAxis>
</ms:Chart>

Tick mark spacing is expressed in terms of post-conversion coordinates. Therefore, to have tick marks appear at every factor of the log base (e.g. every factor of 10), specify a tick mark interval of 1.