Question

The value of $\frac{lo{g}_{2}24}{lo{g}_{96}2}-\frac{lo{g}_{2}192}{lo{g}_{12}2}$ is

• A. $3$
• B. $0$
• C. $2$
• D. $1$

Answer 1

Answer: (A)

$3$

Consider

$\frac{lo{g}_{2}24}{lo{g}_{96}2}-\frac{lo{g}_{2}192}{lo{g}_{12}2}$

$=\frac{log24.log96-log192log12}{(log2{)}^2}$

$=\frac{log(2^3\times 3)log(2^5\times 3)-log(2^6\times 3)log(2^2\times 3)}{(log2{)}^2}$

$=\frac{(3log2+log3)(5log2+log3)-(6log2+log3)(2log2+log3)}{(log2{)}^2}$

$=\frac{15(log2{)}^2-12(log2{)}^2}{(log2{)}^2}$

$=3\frac{\left(log2\right)}{log2}$

$=3$

Option A is the correct answer.