It is also logarithmic (as are all greenhouse gases), but not with the same relationship as that of CO2 at their respective concentrations. At current concentrations I think CH4 would have to be doubled 12 times to create the same 3.7W/m^2 forcing as CO2 does with one doubling.
It’s often noted that methane is “20x more powerful than CO2″ (see a quick google result for proof). This statement can potentially be misleading, so it is worth clarifying just what it means.
The natural 33 K greenhouse effect has a much larger influence from CO2 than it does CH4. Even in the context of how the greenhouse effect is changing, CO2 is currently a much stronger forcing agent than CH4. In what sense is CH4 more powerful? This is only if we compare CO2 and CH4 side-by-side and allow the two gases to change by some incremental amount at existing background concentrations. It is only because CH4 is far less abundant in the atmosphere that adding, say, 1 ppm of CH4 will produce a larger radiative forcing than would be adding 1 ppm of CO2 to today’s atmosphere. This has nothing to do with any intrinsic property of the gas. If CO2 were far less abundant, and CH4 much more abundant, then adding a certain about of CO2 would be more effective at reducing the OLR, and we would then say “CO2 is a more powerful greenhouse gas.”
From: Here
That article and this one should be required reading for everyone interested in the physical basis for AGW.