a,b,c are positive numbers such that they are in increasing Geometric progression then how many such numbers are there in (loga+logb+logc)/6 =log6

• a,b,c are in increasing geometric progression so it will follow the b^2=ac
  as well as it will be in increasing order.
  log(abc)/6 = log6
  so abc=6^6;
  so possible value of a,b,c will be
  1 , 36,36^2
  1/6^2,6^2,6^6
  ......infinite..
  
  there will be another no also but they will not be considered because they are not in increasing order.
• 10 years agoHelpfull: Yes(1) No(0)
• given that a,b,c are in gp
  so b/a=c/b =>b^2=ac
  (loga+logb+logc)/6=log6
  =>log(abc)=6*log6
  =>log(ac*b)=log(6^6)
  =>log(b^3)=log(6^6)
  =>b^3=6^6=>b^3=(6^2)^3
  =>b=6^2=36
• 10 years agoHelpfull: Yes(0) No(2)
• a,b,c are in increasing geometric progression so it will follow the b^2=ac
  as well as it will be in increasing order.
  log(abc)/6 = log6
  so abc=6^6;
  so possible value of a,b,c will be
  1 , 18, 324
  2, 18 , 162
  3, 18 , 108
  6, 18, 54
  9 , 18, 36
  there will be another no also but they will not be considered because they are not in increasing order.
  
• 10 years agoHelpfull: Yes(0) No(1)
• given that a,b,c are in gp
  so b/a=c/b =>b^2=ac
  (loga+logb+logc)/6=log6
  =>log(abc)=6*log6
  =>log(ac*b)=log(6^6)
  =>log(b^3)=log(6^6)
  =>b^3=6^6=>b^3=(6^2)^3
  =>b=6^2=36
  it means a=2,c=18or a=3 c=12 or a=4 c=9 or a=6 c=6.
  hence there are four such numbers
  
• 10 years agoHelpfull: Yes(0) No(0)