Question

8 to power ( x + 1 ) = 16 to power ( y + 2 ) ; 2 to power - (3+ x) = 4 to power - (3y) ​

Answer 1

Answer:

8^(x + 1) = 16^(y+ 2)

2^3(x+1) = 2^4(y + 2)

So , 3x + 3 = 4y + 8

3x - 4y = 5 ...(i)

2^-(3+x) = 4^-3y

2^-(3+x) = 2^-2(3y)

So , - 3 - x = -6y

x - 6y = -3 ...(ii)

Multiply 3 to eq. (ii) and subtract (i) from it

(3x - 18y) - (3x - 4y) = - 3 + 5

3x - 18y - 3x + 4y = 2

-14y = 2

y = -1/7

x + 6/7 = -3

x = -3 - 6/7

x = (-21 - 6) / 7

x = -27/7