Log2_24/log96_2-log2_192/log12_2

1. Для положительных значений a, b и c верны тождества:

loga (b) = 1 / logb (a); (1)

loga (bc) = loga (b) + loga (c). (2)

2. Исходя из формул (1) и (2), получим:

log96 (2) = 1 / log2 (96);

log12 (2) = 1 / log2 (12);

Z = log2 (24) / log96 (2) - log2 (192) / log12 (2);

Z = log2 (24) * log2 (96) - log2 (192) * log2 (12);

Z = log2 (8 * 3) * log2 (32 * 3) - log2 (64 * 3) * log2 (4 * 3);

Z = log2 (2^3 * 3) * log2 (2^5 * 3) - log2 (2^6 * 3) * log2 (2^2 * 3);

Z = (3 + log2 (3)) * (5 + log2 (3)) - (6 + log2 (3)) * (2 + log2 (3);

Z = 15 + 8log2 (3) + (log2 (3)) ^2 - 12 - 8log2 (3) - (log2 (3)) ^2;

Z = 3.

Ответ: 3.