In my teacher's lecture, its have a problems like this: execute statements based on the following base predicates
$L(x)$: $x$ is a logician
$f(x)$: a function that return values is a friend of $x$
So, performs this sentences to logic predicate:
There are some people who are friends of $x$ who are also logicians
The results is: $\exists x L(f(x))$ but its not supposed like this $\exists x, y L(x) \land y = f(x)$?
I dont know why but is this the same or not? Then can I replace nested predicate instead of $\land$, too?
$$\exists x L(f(x))$$
and $$\exists x, y \ L(x) \land y = f(x)$$
are not equivalent: in the second statement, you are saying that $x$ is a logician, but it should be that the friend of $x$ is a logician. So, what you can do is:
$$\exists x, y \ L(y) \land y = f(x)$$
and that statement is equivalent to
$$\exists x L(f(x))$$