weird logarithm rule or illegal move? + parallelogram question help

[vivid oar]

i saw my friend do this with a question and it works but i never saw that method before, i solved the same q using the change of base formula and got the same result. If this is a rule could i see a proof or explain it to me because i don't get it

for the ⏥ question, i asked it before but it didn't get answered, i just want to know if it is poss to do. (it was from my friend who is in another country so i couldnt find the ans for it ( ill send pic soon)

[vivid oar]

this is the parallelogram question

there is english at the bottom of the other language

i dont think it's possible but maybe im dum