Solve for y in the equation 10^1 x 5(2y - 2) x 4(y - 1) = 1

A.

\(\frac{3}{4}\)

B.

\(\frac{5}{4}\)

C.

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

D.

5

Correct answer is C

10y x 5(2y - 2) x 4(y - 1) = 1

but 10y - (5 x 2)y = 5y x 2y

= (Law of indices)

5y x 2y x 5(2y - 2) x 4(y - 1) = 1

but 4(y - 1) = 22(y - 1)

= 2y - 2 (Law of indices)

5y 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 ao = 1

10(3y -2) = 10o

3y - 2 = 0

∴ y = \(\frac{2}{3}\)