Maths-
General
Easy

Question

Solve: 8x.4y = 128 , 92x-y = 1

hintHint:

In Mathematics, lets say, "a" represents a number and "n" is the number of times that number is to be multiplied with itself, in order to get a desired result. Then, such result can be written as an, where a is called the base and n is its power/ exponent.
an = a × a × ... × a                n times.

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





    Step-by-step solution:-
    8x . 4y = 128 …........................................ (Equation i)
       92x-y = 1
    ∴ 92x-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-
       8x . 4y = 128
    ∴ 8x . 42x = 128
    ∴ (23)x × (22) 2x = 128
    ∴ 23x × 24x = 128 .............................. [(bn)m = bnm]
    ∴ 23x+4x = 128 .............................. (an × am = an+m)
    ∴ 27x = 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.

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