If x^y = y^x and x = 2y, the value of y is:
Option 1 : 1 Option 2 : 2 Option 3 : 3 Option 4 : 4 Option 5 :
None of
these

• Ans:-Option2:2
  if y=1, then x=2*1=2 . 2^1=2 &1^2=1
  if y=2,then x=2*2=4. 4^2=16 &2^4=16. equation satiesfied for y=2...
• 9 years agoHelpfull: Yes(8) No(1)
• Options 2 is correct
• 9 years agoHelpfull: Yes(7) No(1)
• x^y=y^x
  2y^y=y^2y
  ylog2y=2ylogy
  log 2+log y=2log y
  log 2=log y
  y=2
• 8 years agoHelpfull: Yes(3) No(0)
• option 2 is the correct answer...
  
• 9 years agoHelpfull: Yes(1) No(0)
• put x=2y
  > (2y)^y = y^2y
  > 2^y * y^y =y^y * y^y
  >2^y = y^y
  y=2
• 8 years agoHelpfull: Yes(1) No(0)
• answer y=1
• 9 years agoHelpfull: Yes(0) No(0)
• on soliving we will get 2^y=y^2....
  so y=2
• 9 years agoHelpfull: Yes(0) No(0)
• Ans: 2
  sub X = 2Y in 1st eqn
  ( 2Y )^Y = Y^(2Y)
  2^Y * Y^Y = Y^Y * Y^Y
  2^Y = Y^Y
  powers are equal so equate the bases
  .". Y = 2
• 8 years agoHelpfull: Yes(0) No(0)
• 2 answer y is 2x so place this in eq anD solve we get 2^y is y ^y then it gives ans
• 8 years agoHelpfull: Yes(0) No(0)
• option 2 is correct.. y = 2
  x^y = y^x
  taking log on both sides...
  y log x = x log y
  putting x = 2y we get,
  y log 2y = 2y log y
  log 2y = 2 log y
  log 2y = log y^2
  2y = y^2
  y = 2
• 8 years agoHelpfull: Yes(0) No(0)
• option 2: 2
  x^y=y^x and x=2y...from that (2y)^y=y^(2y)......(2^y)(y^y)=(y^y)(y^y)...then
  2^y=y^y....then 2=y..........
• 8 years agoHelpfull: Yes(0) No(0)
• for y=2 the value of x^y andy^x will be satisfied so the value of y will be 2
• 7 years agoHelpfull: Yes(0) No(0)