Question

Given that 2^x = 8^y+1 and 9^y = 3^x-9, then the value of x + Y is

Answer 1

Answer: 27

Step-by-step explanation:

$2^x = 8^{y+1}\\2^x = (2^3)^{y+1}\\2^x = 2^{3y+3}\\x=3y+3\\x-3y=3$......... (1)

$9^y=3^{x-9}\\(3^2)^y=3^{x-9}\\3^{2y}=3^{x-9}\\2y=x-9\\x-2y=9$....... (2)

Solving (1) and (2), we get : x = 21 and y =6

so x+y = 21 +6 =27