Reduce to the simplest form: log2(24)/log96(2) -log2(192)/log12(2)

We'll write log 2 (24), using the product rule of
logarithms:

log 2 (24) = log 2 (2) + log 2
(12)

We'll write log 96 (2) = 1/ log 2
(96)

log 2 (96) = 1 + log 2 (2) + log 2 (2) + log 2
(12)

log 2 (96) = 3 + log 2
(12)

log 2 (192) = 4 + log 2
(12)

log 12 (2) = 1/ log 2
(12)

We'll re-qrite the
expression:

E = [1 + log 2 (12)][3 + log 2 (12)] - [4 + log
2 (12)]*log 2 (12)

We'll remove the brackets and we'll
replace log 2 (12) by t:

E = 3 + 4t + t^2 - 4t -
t^2

We'll combine and eliminate like
terms:

E = 3

The
given expression reduced to the simplest form is E =
3.