Is the phrase below correct?
I have tried to contact the customer without success.
Isn't it "I have tried to contact the customer unsuccessfully"?
Both are bad. The first suggests you might have tried to fail, the second either
What I assume you want to say is that you tried (fair and square), but did not get through – the attempt was unsuccessful.
It would be better to write either:
Part of the ambiguity of your sentence (as mentioned in the answers from Daniel and Born2Smile) could be avoided by rearranging it slightly:
The subordinate clause "without success" could then be replaced by "unsuccessfully" without changing the meaning of the sentence, and it would be clear that the lack of success pertains to your attempt to contact the customer, not to the customer.
Personally, I fail to see how one can read either of your sentences (or my modified example for that matter) to mean that you have "tried to fail", since the adverb "unsuccessful" (or the adverbial clause "without success") clearly pertains to the verb "to try".
So, to answer your original question, neither of your sentences is incorrect, but some slight ambiguity of your first one could be overcome by rephrasing/rearranging it slightly.
They are both correct. Unsuccessfully is an adverb which means the same thing as the prepositional phrase without success.
However, as Born2Smile points out, they could possibly be construed to mean "I have tried to be unsuccessful in contacting the customer". To avoid this very slight confusion, you could say I have unsuccessfully tried to contact the customer or I have tried to contact the customer, but have been unsuccessful.
To me, both sound incorrect.
'unsuccessfully' and 'without success' both mean the same and can be interchangeably used in most scenarios.
However, "I have tried to contact the customer without success" or "I have tried to contact the customer unsuccessfully" both imply your attempt (try) was without success/unsuccessful, whereas, what you want to convey is that you had tried to contact the customer, and were unsuccessful at contacting, not trying.
I would say: "I tried to contact the customer but was unsuccessful". Or, if you are not too attached with success (pun unintended), "I tried to contact the customer but couldn't".