Please show all work and label problems as you go along... I need to understand this stuff !
Explain how you did the problem!

paying 22 fg

I wish I could help, the first initial wording is weird. I have never been taught logarithms through such a format.

However, Logb A + Logb C = Logb(AC), so lets plug and chug; log12 9 + log12 16 = log12(9*16)

log12(9*16) = log12(144)

Here, we can use the change of base formula, which is LogD B = log B/log D. (or we can simply see that 12^2 = 144, therefore answer is 2.

Log12(144) = log 144/log 12 = 2

First is solved.

Second :

just expand Log ( x² / yz^3 ) = Log ( x² ) - Log ( y ) - Log ( z^3 ) = 2xLog ( x ) - Log ( y ) - 3xLog ( z )

(assume all quantities x, y and z are striclty positive).

Third :

Ln( a+b) + Ln(a-b) - 2 Ln(c) = Ln [ (a+b)x(a-b)] - Ln(c²) = Ln [ (a+b)(a-b) / c² ] = Ln [ (a² - b²) / c² ]

Fourth : is it Log (2) with base 5 ?

If so, Log (2) = Ln (2) / Ln (5) ~ 0.430677