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 = \(\frac{2}{3}\)