text: 1. ## Given 2^x=8^(y+1)...
  
  Given 2^x=8^(y+1) and 9^y=3^(x-9), find the value of x+7.
  
  2. Originally Posted by ceasar_19134
  Given 2^x=8^(y+1) and 9^y=3^(x-9), find the value of x+7.
  2^x = 8^(y+1) is 2^x = 2^(3y+3) or x=3y+3.
  9^y=3^(x-9) is 3^(2y) = 3^(x-9) or 2y=x-9.
  Now solve that system.
  
  3. 2^x = 8^(y+1) is 2^x = 2^(3y+3) ---> x=3y+3.....(1)
  9^y=3^(x-9) is 3^(2y) = 3^(x-9) ---> 2y=x-9......(2)
  
  (x-3)/3 = y
  
  substitute this into (2)
  
  (2x - 6)/3 = x - 9
  2x - 6 = 3x - 27
  x = 21 (and y = 6)
  therefore