Question

Me pueden ayudar en este ejercicio?

Answer 1

[2^(2X - 3)]/[2^(3Y + 2)] = 2^8 (Ecuacion 1)

3X - 2Y = 17 (Ecuacion 2)

3X = 2Y + 17

X = 2Y/3 + 17/3

Reemplazo X en la ecuacion (1)

[2^(2X - 3)]/[2^(3Y + 2)] = 2^8

[2^(2(2Y/3 + 17/3) - 3)]/[2^(3Y + 2)] = 2^8

[2^(4Y/3 + 34/3 - 3)]/[2^(3Y + 2)] = 2^8

[2^(4Y/3 + 34/3 - 3)]/[2^(3Y + 2)] = 2^8

[2^(4Y/3 + 25/3)]/[2^(3Y + 2)] = 2^8

[2^(4Y/3 + 25/3)]*1/[2^(3Y + 2)] = 2^8

[2^(4Y/3 + 25/3)]*[2^-(3Y + 2)] = 2^8

2^[(4Y/3 + 25/3) - (3Y + 2)] = 2^8

Aplicamos la siguiente propiedad:

a^f(x) = a^g(x)

f(x) = g(x)

[(4Y/3 + 25/3) - (3Y + 2)] = 8

4Y/3 + 25/3 - 3Y - 2 = 8

4Y/3 - 3Y + 25/3 - 2; 4Y/3 - 9Y/3 = -5Y/3

25/3 - 2 = 25/3 - 6/3 = 19/3

-5Y/3 + 19/3 = 8

-5Y + 19 = 24

 19 - 24 = 5Y

-5 = 5Y

Y = -5/5

Y = -1

Rta: A