Question

2 to the power x+y = 128 and 4 to the power x-y = 16, so find x/y is

Answer 1

4^(x-y)=16

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

Since based are same then powers must be equal

So, x-y=2

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

2^(x+y)=128

=2^(x+y)=2^(7)

Since based are equal so the powers must be equal

So,

x+y=7

x+(x-2)=7........from (1)

2x-2=7

2x=9

x=9/2 and y=x-2=9/2-4/2=5/2

x/y=9/2÷5/2=9/5

I hope it will help you ☺

Answer 2

Hi Mate:-


$2 {}^{x + y} \: = \: 2 {}^{7} .......because \: 2 {}^{7} = 128 \\ and \\ \\ 4 {}^{x - y} \: = \: 4 {}^{2} ........because \: \: 4 {}^{2} \: = \: 16 \\ \\ = > \\ \\ x + y = 7 \\ and \\ \\ x - y = 2 \\ \\ now \: adding \: both \: the \: equations \\ \\ 2x = 9 \\ x = 9 \div 2 \\ and \\ y = 5 \div 2 \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \: \: \: \: \: \: hope \: it \: helps$