linear trendlines on log plot

how can I put an linear trendline for a part of my data series that is linear when most of the plot is logarithmic.

Didn't quite understand what you want, but I don't think you can base a trendline on part of a data series. If you want to base a trendline on part of a data series, create a new series that consists only of the data you desire to fit. If needed, make this series "invisible" with no marker and no line.