Spacing of Abbreviated Function Names

Hi, I have question about the Spacing of Abbreviated Function Names.
From NFB Nemeth lesson 14.3 "Spacing of Abbreviated Function Names Within a mathematical expression, the following spacing rules are observed. These rules apply regardless of the spacing used in the print copy.
a. No space comes before an abbreviated function name unless it follows a sign of
comparison or other symbol that requires spacing.
b. A space is required after an abbreviated function name or its inverse (the space follows the
superscript). There is one exception – see 14.3.2, below. "

However, I was wondering how to handle the spacing in these cases. Please see the attached file. If I applied the wrong rules, please let me know which ones I should review.

Thank you for your help!