If 2^x=8^(y + 1)
& 9^y = 3^(x – 9)
Find y

• 2^x=8^(y + 1)
  
  or 2^x = (2^3)^(y+1) = 2^(3y+3) ... Bases are equal, powers must be equal.
  so x= 3y+3 ....... (1)
  
  & 9^y = 3^(x - 9)
  (3^2)^y = 3^(x-9)
  3^2y = 3^(x-9).... bases are equal. so powers must also be equal.
  2y = x-9 ......... (2)
  
  From (1) and (2)
  2y = 3y+3-9= 3y-6
  y=6
  and hence
  x= 21.
• 12 years agoHelpfull: Yes(7) No(1)
• Y = 6
  
  Question :
  If 2^x = 8^(y + 1) & 9^y = 3^(x - 9). Find y
  
  Answer :
  
  2^x = 8^(y + 1) ---->(1)
  9^y = 3^(x - 9) ---->(2)
  
  Put Y=6 in condition(1)
  2^x = 8^(6+1)
  2^x = 8^7
  2^x = 2097152
  
  2^21 = 2097152. (So, x=21).
  
  Apply x=21 value in Condition(2)
  9^y = 3^(x-9)
  9^y = 3^(21-9)
  9^y = 3^(12)
  9^y = 531441
  
  9^6 = 531441 (Y=6; X=21)
  Conditions Satisfy.
  
  So, Y=6; X=21;
  
  
• 12 years agoHelpfull: Yes(3) No(3)
• y=6
  
  Well explained by Aman.
• 12 years agoHelpfull: Yes(3) No(0)
• If anybody have easy explanation to solve this question.
  Take my answer as reference and worked out.
  Thank you:)
  
• 12 years agoHelpfull: Yes(1) No(1)