The phrase "as the only logical" is correct and usable in written English.
It can be used when presenting a conclusion or reasoning that is deemed the most rational or sensible option among alternatives.
Example: "Given the circumstances and available data, pursuing this course of action is as the only logical choice."
Alternatives: "as the sole rational" or "as the most reasonable".
Excessive in himself, he has always inspired hyperbole in others as the only logical method of dealing with his special case.
I expect even lower prices in coming months as the only logical market response to a persistent over-supply of oil in the world and a weak global economy.
Google countered that the two firms should have tried to negotiate a deal based on the starting point of a 2.25% royalty demand, which it described as "the only logical starting point" since it had agreed other licences on this basis.
The Invasion addresses how those elements are quickly and forcefully weaved into society, establishing themselves as the only logical recourse.
It is, rather, to point out that Wall Street gamblers have made the solution relatively simple by digging their own grave, doomed themselves to bankruptcy, thereby leaving nationalization as the only logical or viable solution.
A continual cycle of modeling, hypothesis generation, experimentation, and model refinement is proposed as the only logical way for biology to move forward.
The all-electronic Nasdaq was once regarded as perhaps the only logical home for technology listings.
One hesitates to dive into anyone else's mind on the basis of a few words (remember trying to interpret Eric Cantona's famous "when the seagulls follow the trawler" speech back in 1995?); but as far as I can see, the only logical explanation is that the writer thinks curbing grenhouse gas emissions will cost so much that the developing world will be left poverty-stricken as a result.
It is of great concern to me that you do not have a similar reaction, as it seems the only logical response to such horrors.
It has been shown that abductive reasoning plays a key role in design as it is the only logical operation that introduces new ideas.
Since Parcells is on record as saying he wants to do anything that is needed for his new friend and new owner, Woody Johnson, Parcells is the only logical short-term solution, as long as his cardiologist gives his approval.
