in the end vs at long last

in the end and at long last both are adverbs.

Word	Noun	Adjective	Verb	Adverb
in the end	No	No	No	Yes
at long last	No	No	No	Yes

As adverbs, in the end and at long last are synonyms defined as:

in the end and at long last: as the end result of a succession or process

Other synonyms of in the end include at last, finally, ultimately.

in the end (adverb)	at long last (adverb)
as the end result of a succession or process	as the end result of a succession or process
eventually or after a lengthy period of time