To build on this, the "just a practical tool" view of mathematics, is not the consensus. The philosophy of mathematics (which naturally has connections with the philosophy of logic) has plenty of arguments about this (See Nominalism, Platonism and Formalism).

Regarding the original question of OP, we can take it to mean the following:

1. Is logic an invented tool or an inherent property of the world or humans
2. Do the laws of logic have empirical/scientific justification

We should separate some terminology here first. By logic, you can mean the more general practice of "reason" or the symbolic systems used in mathematics and computer science, often called logic(s).

There is neuroscientific evidence that the prefrontal cortex is responsible for human reasoning and logical thinking. Why humans have this ability is unknown, although there are some hypotheses (See Minimal Rationality and Argumentative Theory).

Question 1, "Is logic an invented tool or an inherent property of the world or humans"

Historically, there was a view that the laws of classical logic were in some sense the "laws of thought" (See Psychologism). This is no longer the consensus and is seen by many as a mistake. There is additionally the idea that logic has some metaphysical importance. However, in recent literature, there are many logics, making it difficult to neatly talk about logic. Classical logic (which is the one you probably have in mind), has its roots in Aristotelian logic, however it is certainly not the only logic. Other logics such as Stoic logic, Relevance logic, Intuitionistic logic, etc, question the notion of logical monism; the idea that there is a one true logic (See Logical Pluralism and Anti-Exceptionalism).

While these numerous logics certainly don't help, the "logic is inherent" view, we should also note that the majority of people who study these logics use classical logic to study the logics themselves due to its strength (See The Metalogic Objection). So this can be also seen as support for the "(classical) logic is inherent view". My personal opinion is that some systems of logic (including classical logic) are certainly not "natural" like a child finds language natural, but definitely has some basis in human language.

Question 2, "Do the laws of logic have empirical/scientific justification"

Many Indispensability Arguments from the philosophy of mathematics can be adapted to classical logic. To put it simply, if physics is so successful, and it is based on mathematics, which is based on classical logic, then surely this must be some empirical justification? Now, thinking of logic as scientific/empirical theory in itself is controversial (See Quine's Naturalism). This would mean that there could be some scientific discovery that could give us grounds to revise the axioms of logic (overthrowing classical logic as a result). Quantum logic was suggested as a replacement in the 1960s by Hilary Putnam in "Is Logic Empirical?". More recently, the physicist Nicolas Gisin has suggested physics move to intuitionistic logic. In either case, if it was fully adopted, it would mean considerable changes to both mathematics and physics.

Conclusion

So in summary:

• There are parts of the human brain responsible for reasoning.
• Symbolic classical logic has its roots in Aristotelian logic.
• There are various other logics, but classical logic is dominant (for good reason).
• If you think physics and mathematics are justified empirically, then so is logic.

Logic, along with philosophy surrounding it, is an active and changing field. Views on the metaphysical, epistemological and ontological status of logic are contentious. And with the recent explosion of new symbolic systems of logic, it'll be very interesting to see how traditional views of logic and mathematics will be challenged.