You've 'based' your opinion 'on' faulty information. = Your opinion is 'based on' faulty information. [=the information that you used to form your opinion is wrong]
The company's 'base' is in London. = The company's 'base of operations' is (in) London. [=the company's main offices are in London]
Although I disagreed with the book's theoretical 'base' [='basis, foundation'], I couldn't really find fault with its logic.
(..) Tells this cute little tattle-tales to sell his junk, but he don't sell no Yankee boys no truth. Something happened, right? It had to be based on some real incident. Are you, Jimmy Olsen, cub reporter for the Daily Asshole? - Grampa, watch your language. - I don't think you need to know. (..)2003 House of 1000 Corpses
(..) We gotta move! He's gonna blow the columns! My God! - Mo'at! No! - Lf you are one of us, help us. All call signs, switch missiles. Give me HE's at the base of the west columns. This way! Rider section, switch missiles. - One's good. - Two's rocks up. - Three's up. - Yeah, baby, get some! (..)2009 Avatar
(..) another begins. Harnesses off! Get your packs! - Put it together, let's go! Let's go! - Harnesses off! One minute! When that ramp comes down, go directly into the base. Do not stop! Go straight inside. Wait for my mark! Go, go, go, go! Get out of there! Keep moving! Let's go, let's go! (..)2009 Avatar