Question

80. (x & x-2 is power)
The real number x satisfying 2x - 2x - 2= 192 is :
(A) 7
(B) 8
(C) 9
(D) 10​

Answer 1

Answer:

${2}^{x} - {2}^{x - 2} = 192$

${2}^{x} (1 - {2}^{ - 2} ) = 192$

${2}^{x} (1 - \frac{1}{ {2}^{2} } ) = 192$

${2}^{x} (1 - \frac{1}{4} ) = 192$

${2}^{x} ( \frac{4 - 1}{4} ) = 192$

${2}^{x} \times \frac{3}{4} = 192$

${2}^{x} = 192 \times \frac{4}{3}$

${2}^{x} = 64 \times 4$

${2}^{x} = 256$

${2}^{x} = {2}^{8}$

$x = 8$