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The value of ((log)2 24)/((log)(96)2)-((...

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

A

3

B

0

C

2

D

1

Text Solution

Verified by Experts

The correct Answer is:
A
Let ` log_(2) 12 =a`, then
` 1/(log_(96)2) = log_(2) 96 = log_(2) 2^(3) xx 12 = 3 + a`
` log_(2) 24=1+a`
` rArr log_(2) 192 = log_(2) (16xx12) = 4 + a`
` and 1 /(log_(12)2) = log_(2) 12 = a` .
Therefore, the given expression is:
` (1+a)(3+a)-(4+a) a = 3`
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