Question

2^x = 4*2^y , 9*3^x = 3^-y

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

x = 0 and y = -2

Step-by-step explanation:

2^x = 4*2^y

2^x ÷ 2^y = 4

2^(x-y) = 2^2

Here, bases are equal so we can compare their powers.

Therefore,

x-y = 2 ............ (1)

Now,

9*3^x = 3^-y

9*3^x = 1/3^y

(x^-1 = 1/x)

3^x * 3^y = 1/9

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

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

Here again, bases are equal so we can compare their powers.

Therefore,

x+y = -2 ............ (2)

By adding equation (1) and (2),

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

2x = 2-2

2x = 0

x = 0

By putting this x = 0 in equation (2)

x+y = -2

0+y = -2

y = -2

Answer : x=0 and y = -2