The value of `((log)_2 24)/((log)_(96)2)-((log)_2 192)/((log)_(12)2)` is 3 (b) 0 (c) 2 (d) 1

Explanation

`[log_2^24*log_2^96]-[log_2^192]*[log_2^12]`

`[log_2^(2^2*3)]*[log_2^(2^5^3)]*[log_2^(2^6*3)]*[log_2^(2^2*3)]`

`[log_2^(2^3)+log_2^3][log_2^(2^5)+log_2^3)]-[log_2^(2^6)+log_2^3]*[log_2(2^2)+log_2^3]`

`[3+log_2^3][5+log_2^3]-[6+log_2^3][2+log_2^3]`

`15+8log_2^3+(log_2^3)^2-12-8log_2^3-(log_2^3)^2`

`=15-12`

`=3`

Option A is correct.