Are "like" and "such as" completely synonymous?
Solution 1:
Both like and such as can be used to introduce examples. This is what's going on in these two sentences that you gave:
A friend like you is a treasure / A friend such as you is a treasure
I hate tests like these / I hate tests such as these
However, such as cannot be used to join two things which are similar---only like can be used in this case:
No one cares like you / *No one cares such as you
In this sentence, the intended meaning is something like No one cares in the way that you do, and only like can be used for this purpose.
Note that I'd put for first example in this category:
I want a cookie like that
? I want a cookie such as that
It seems to me that this means I want a cookie similar to that one, and such as strikes me as ungrammatical to use here.
Solution 2:
I've read something about it when I was looking for some prep for GRE verbal exam:
Like is used to describe something that resembles something else.
He runs like a rabbit.
Such as is used in situations where the object of comparison is certain.
At the zoo I saw animals such as lions and elephants.
Take the last example:
1) At the zoo I saw animals such as lions and elephants.
2) At the zoo I saw animals like lions and elephants.
The first means that I in fact saw lions and elephants whereas the second implies that I saw animals similar to lions and elephants. Maybe tigers and rhinos.
and...
"Writers whom we respect disagree on whether there is any significant difference between like and such as. Wilson Follett and Theodore Bernstein say no. James J. Kilpatrick says yes. We come down gingerly on the side of Kilpatrick. His argument seems valid: 'When we are talking of large, indefinite fields of similarity, like properly may be used. . . . When we are talking about specifically named persons [places or things] . . . included in a small field, we ought to use such as.' In 'Books like this one can help you write better,' like means similar to. In 'Cities such as Atlanta and Birmingham are important to the economy of the Southeast,' the intent is to specify those cities as examples, not merely to put them into a broad category of cities that are important to the economy of the Southeast" (Lederer and Dowis, Sleeping Dogs Don't Lay 79).
it sounds like "let me Google it for you!"
Good luck
Solution 3:
Friendship such as that is not helpful.
Sounds OK to me.