Express As A Single Log

log(a) + log(b) = log(ab)

Tell me...
Does the provided log rule apply to question 1 or 2?

Both.

8log(sqrt{3x-2}) - log(4/x) + log(4) =
log(sqrt{3x-2}^8) - log(4/x) + log(4) =
log({3x-2}^4) - log(4/x) + log(4) =
log(4) + log({3x-2}^4) - log(4/x) =
log(4 * {3x-2}^4 / {4/x}) =
log(x * {3x-2}^4)

2*log(5x^3) - 0.5*log(2x + 3) =
log({5x^3}^2) - log(sqrt{2x+3) =
log(25x^6) - log(sqrt{2x+3}) =
log({25x^6} / sqrt{2x+3})

In addition to
log(a) + log(b) = log(ab)
you also needed
a*log(b) = log(b^a)

Great
Great work and clarity.