Log or find what and which text a SMS app sent?
First, I'd report that app as fraud to Google: such behavior IMHO contradicts with their rules (you can also give the appmaker the option to either have you removed from that subscription, or you would report – with the latter resulting in his app being removed from Play).

Second, if you don't need premium SMS services in general, check with your provider to have them removed altogether. If you can convince them you cannot unsubscribe due to fraudulent behavior of an app having you subscribed to and not letting you unsubscribe, it's their duty to take care for it (to do so, they don't need to reveal that "servicename" to you, as long as they stop charging you). Otherwise you could report them to the corresponding regulation office.

Having premium services disabled altogether should stop them from charging you. After that, if you don't want to read messages coming from that dubious service, you can simply put their number on your blacklist.