
A.
(frac{3}{4}) 
B.
(frac{5}{4}) 
C.
(frac{2}{3}) 
D.
5
Correct Answer: Option C
Explanation
10^{y} x 5^{(2y – 2)} x 4^{(y – 1)} = 1
but 10^{y} – (5 x 2)^{y} = 5^{y} x 2^{y}
= (Law of indices)
5^{y} x 2^{y} x 5^{(2y – 2)} x 4(y – 1) = 1
but 4^{(y – 1)} = 2^{2(y – 1)}
= 2y – 2 (Law of indices)
5^{y} x 5^{(2y 2)} x 2^{( 2)} = 1
5^{(3y 2)} x 2y x 2^{(2y 2)} = 1
= 5^{(3y 2)} x 2^{(3y 2)} = 1
But a^{o} = 1
10^{(3y 2)} = 10^{o}
3y – 2 = 0
∴ y = (frac{2}{3})