In the following sentence, I'm unable to understand why the article "den" is used.
Karl und Susanne suchten eine Weile nach Informationen in den Büchern.
Also why is "Bücher" declined with an "n". "Buch" is neutral but multiple books would be feminine: Bücher. "In" is dative so I would think it would use the feminine, dative article: "der". I know it can be declined with "n" in weak declensions but does that apply here? Help🙄
Nouns in German have grammatical Gender, case, and number (singular vs. plural). All three of these affect the word ending, but in practice you can merge grammatical gender and number into four "classes", masculine singular, feminine singular, neuter singular, and plural. You seem to have noticed that The feminine singular and plural have a lot in common, but they are not the same. Your question points to one of the differences, feminine singular nouns generally do not end with '-n' in the dative case, while plural nouns generally do end with '-n' in the dative. In fact the rule for forming the dative plural is relatively simple in German: Add "-n" to the nominative plural if it doesn't already end in "-n". This applies to almost all nouns except for certain borrowed words, and a few native words, whose plural ends in "-s": "Ich bin bei den Autos.", "Ich bin bei den Omas." The way "Buch" forms its plural is not the most common, but it's not rare either: "Buch" - "Bücher", "Dorf" - "Dörfer", "Haus" - "Häuser".
For the first question, why "den", it turns out that "den" is used for both masculine (singular) accusative and plural dative. Note that the feminine singular dative form is "der", another difference between feminine and plural. It seems odd if your starting German that the same word, "den", is used for two unrelated declensions. There are historical reasons for it, but you basically have to just memorize the table, even though there are seemingly random "duplicates". The good news is that knowing it will help make sense of other declensions, including adjectives and certain pronouns.
"Buch" is neutral but multiple books would be feminine: Bücher. "
I don't know how you came to this assumption, but that's not how this works. Multiple books aren't feminine, they are still neutral (sächlich) but in plural. The article for plural in nominative case happens to be "die", but in dative case, there's a difference in articles between female and plural. Studying declension tables for nouns of different gender, for example on Wiktionary, should make the difference clear. There's always a singular and a plural part.
