Question

8^x * 4^y = 128 9^(2x-y)=1 find x and y​

Answer 1

8^x*4^y=128 =>

(2^3^x) * (2^2^y) = 2^7 =>

(2^3x)*(2^2y) = 2^7 =>

2^(3x+2y) = 2^7 =>

3x+2y = 7

Finding the possibilities for ‘x’ and ‘y’ in trail and error method, the most common possibility for the above equation is,

x = 1 & y = 2.

To verify this we can substitute the same result in second give equation as 9^x+y=27^xy

9^1+2 = 27^1*2

9^3 = 27^2

729 = 729

So the answer is x = 1 & y = 2.