Question

Вычислить: (log2 192/ log12 2) - log2 24/ log96 2.

Answer 1

$\frac{log_2192}{log_{12} 2}-\frac{log_2 24}{log_{96}2}=log_2(3*2^6)log_2(3*2^2)-log_2(3*2^3)log_2(3*2^5)=\\=(log_23+6)(log_23+2)-(log_23+3)(log_23+5)=\\=log_2^23+8log_3+12-log_2^23-8log_23-15=-3$