adjudge, a judge

A judge or a judge ( two words ) means one ( a ) public official who hears cases in a court, and administers the law ( judge )--
The retired lawyer will soon become a judge.
The case will be heard by a judge, but the jury will decide the outcome.

A judge may also be someone who decides the winner of a contest, or who offers an informed opinion--
He will be a judge at the next gymnastics competition.
As a judge of horses, he's an expert.

Adjudge or adjudge ( one word, rhymes with a judge ) means to decree or to pronounce formally, as from a court or some official position--
We hope the court will adjudge the most recent will to be valid.
The court may adjudge court costs to him, as well as an award.

Adjudge may also mean to consider or decide, in a more general sense--
A prudent person would adjudge it wise to avoid the situation.

Now that you know that, you can say--
"Only a judge may adjudge the legal merits of a request for a search warrant."

Note--"judge" also means to try a case, or to determine the relative merits of contestants in a competition--
She will judge the contestants at the next event.