We have to simplify log(2) 24 / log(96) 2 - log(2) 192 / log(12) 2

log(2) 24 / log(96) 2 - log(2) 192 / log(12) 2

use the property of logarithms: log(a) b = 1/log(b) a

=> log(2) 24* log(2) 96 - log(2) 192 * log(2) 12

=> log(2) 12*2 * log(2) 96 - log(2) 96*2 * log(2) 12

=> [log(2) 12 + log(2) 2]* log(2) 96 - [log(2) 96 + log(2) 2]* log(2) 12

=> log(2) 12 * log(2) 96 + log(2) 2 * log(2) 96 - log(2) 96 * log(2) 12 + log(2) 2* log(2) 12

=> log(2) 12 * log(2) 96 + log(2) 96 - log(2) 96 * log(2) 12 - log(2) 12

=> log(2) 96 - log(2) 12

=> log(2) [ 96/12]

=> log(2) 8

=> 3

**The simplified form of log(2) 24 / log(96) 2 - log(2) 192 / log(12) 2 = 3**

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