It can be seen that the function log(1/x-1) is convex with respect to variable x, but i wonder to konw that how to express this function in the CVX？Many thanks!

How do conclude that it is convex? See

Edit:

Note

ln(1/x-1) =ln((1-x)/x)=ln(1-x)-ln(x)

from which it is easy to prove the non convexity too.

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ohhhhh! I checked my derivation and found some errors.It’s not convex!Thank you very much!