Solve: 8^x.4^y = 128 , 9^2x-y = 1

The correct answer is: Value of x & y for the given equations are 1 & 2, respectively.

Step-by-step solution:-
8^x . 4^y = 128 …........................................ (Equation i)
   9^2x-y = 1
∴ 9^2x-y = 9⁰ …........................................... (b⁰ = 1)
∴ 2x-y = 0 …............................................ (Exponents of the same base of an equation are equal)
∴ 2x = y ............................................... (Equation ii)
Substituting Equation ii in Equation i, we get-
   8^x . 4^y = 128
∴ 8^x . 4^2x = 128
∴ (2³)^x × (2²) ^2x = 128
∴ 2^3x × 2^4x = 128 .............................. [(bⁿ)^m = b^nm]
∴ 2^3x+4x = 128 .............................. (aⁿ × a^m = a^n+m)
∴ 2^7x = 2⁷
∴ 7x = 7 .................................. (Exponents of the same base in an equation are equal)
∴ x = 1 ................................... (Dividing both the sides by 7) ............................................ (Equation iii)
Substituting Equation iii in ii, we get-
2x = y
∴ 2 (1) = y
∴ 2 = y
i.e. y = 2
Final Answer:-
∴ Value of x & y for the given equations are 1 & 2, respectively.