a^x=b, b^y=c, c^z=a ..then what is the value of x*y*z?.

• ANS:1
  if a^x=b , then x=log b/log a
  similarly y= log c/log b
  z=log a / log c
  therefore x*y*z = 1
• 11 years agoHelpfull: Yes(34) No(0)
• ans is 1, take a^x=b now log both side xloga=logb from here we get x=logb/loga, similary we get y=logc/logb and z=loga/logc, now x*y*z=1;
• 11 years agoHelpfull: Yes(5) No(0)
• a^(x*y)=c,a^(x*y*z)=a,
  x*y*z=1(since bases are equal so powers should be equal)
• 11 years agoHelpfull: Yes(3) No(0)
• Here we go:
  
  Put "log" on all three equations:
  
  They will appear as:
  x=(log b/log c) ; y= (log c/log b); z=(log a/log c)
  
  x*y*z=1
  
  Answer : 1
• 11 years agoHelpfull: Yes(1) No(0)
• 1
  taking log both sides
  x loga=logb => x=logb/loga
  y logb=logc => y=logc/logb
  z logc=loga => z=loga/logc
  x*y*z=logb/loga*logc/logb*loga/logc=1
• 11 years agoHelpfull: Yes(1) No(0)
• if x=y=z=1
  then a=b=c
  so this satisfy the condition so
  xyz=1...............
• 11 years agoHelpfull: Yes(1) No(0)
• a^x=b
  b^y=(a^x)^y
  c^z=a=((a^x)^y)^z
  hence x*y*z=1
  
• 11 years agoHelpfull: Yes(1) No(0)
• (((a^x)^y)^z)=a
  =>xyz=1
• 11 years agoHelpfull: Yes(0) No(0)
• step1:- taking log both side:-
  
  log(a^x)=logb, log(b^y)=logc,log(c^z)=loga
  
  step2:-
  x*loga=logb,y*logb=logc,z*logc=loga
  
  step3:-
  x=logb/loga,y=logc/logb,x=logc/loga
  
  put all this value in eq x*y*z
  nd ans is 1..
• 11 years agoHelpfull: Yes(0) No(0)
• a^x=b taking log both side
  x=logb/loga
  simillarly y=logc/logb and z=loga/logc
  So x*y*z=1... Ans: 1
• 11 years agoHelpfull: Yes(0) No(0)