Question

Select the correct option: If $2^x - 2^{x-2} = 192$, the value of x is
A. 5
B. 6
C. 7
D. 8

Answer 1

Option ( D ) is correct.

Explanation :

2^x - 2^x - 2 = 192

=> 2^x - 2^x/2² = 192

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We know the , exponential laws:

i ) a^m-n = a^m/a^n

ii ) If a^m = a^n then m = n

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Let a = 2^x -----( 1 )

Now ,

a - a/4 = 192

=> ( 4a - a )/4 = 192

=> 3a/4 = 192

=> a = ( 4 × 192 )/3

=> a = 4 × 64

=> a = 2² × 2^6

=> a = 2^2+6

=> a = 2^8

2^x = 2^8 [ from ( 1 ) ]

=> x = 8

••••••

Answer 2

Step-by-step explanation:

option d is correct answer