Question

Given that (2*(x -3) ) / 8*( 2 y - 3) = 16*( x - y )​

Answer 1

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

The two are common so we give it out then

x - 3 ÷ 6y - 9 =4x - 4y

x - 3 -4x - 4y = 6y -9

-3x -2y = -6

6=3x+2y

Answer 2

Explanation:

`(2^(x-3))/(8^(2y-3))=16^(x-y)\\\\(2^(x-3))/((2^(3))^(2y-3))=(2^(4))^(x-y)\\\\(2^(x-3))/(2^(3*(2y-3)))=2^(4*(x-y))\\\\(2^(x-3))/(2^(6y-9))=2^(4x-4y)\\\\2^(x-3 -(6y-9))=2^(4x-4y)\\\\2^(x-3-6y+9)=2^(4x-4y)\\\\2^(x-6y+6)=2^(4x-4y)`

base is same, so equate the powers

x - 6y + 6 = 4x - 4y

Subtract 'x' from both sides

-6y + 6 = 4x -x - 4y

-6y + 6 = 3x - 4y

Add '6y' to both sides

6 = 3x - 4y + 6y

6 = 3x + 2y

Hence proved