Difference between Rationally and Logically

RATIONALLY vs LOGICALLY: ADVERB

In a rational manner; in consistency with reason; reasonably: as, to speak rationally; to behave rationally.
According to ratios or proportions.
In mathematics, as a rational function.

According to logical principles, or by formally valid inference: as, to argue logically.

Pragmatically, Objectively, Sustainably, Soundly, Legitimately, Reasonably, Wisely, Efficiently, Judiciously, Effectively, Coherently, Intelligently, Prudently, Sensibly, Logically

Understandably, Arguably, Straight, Surprisingly, Consistently, Obviously, Rightly, Ideally, Clearly, Naturally, Reasonably, Sensibly, Intuitively, Coherently, Rationally

Intuitively, Responsibly, Realistically, Thoughtfully, Analytically, Objectively, Legitimately, Reasonably, Wisely, Efficiently, Judiciously, Coherently, Prudently, Sensibly, Logically

Dialectically, Probabilistically, Theoretically, Analytically, Conceptually, Objectively, Arguably, Straight, Surprisingly, Obviously, Ideally, Reasonably, Sensibly, Intuitively, Coherently

It helps us think more clearly and rationally.
If you think rationally at all, that is.
Do you take your decision intuitively or rationally?
How do you train yourself to trade rationally?
How to gamble and make other decisions rationally.
If rationally related to a legitimate government purpose.
Behave rationally in the face of market volatility.
Member rationally, researchers also characterize communication as inescapable.
Standard economic theory assumes that people behave rationally.
The point is that both believers and unbelievers are able to think rationally so each behaves rationally.

It logically refers to whoever contested the will.
What should logically be coming down the road?
The letter should be logically structured and organized.
In particular, he cannot do the logically impossible.
Columns are logically arranged from left to right.
Now it is logically true that both Christianity and Islam could be wrong, but it is logically impossible to assert that both are true.
All trusted components should be logically separated from each other and shall be logically separated from any untrusted components of the CA system.
In other words, the argument is not logically valid, and its premise does not logically imply its conclusion.
So in order to study anything logically we have to forget the pesky details that prevent things from behaving logically.
The existence of an unlimited being is either logically necessary or logically impossible.