a b c r in gp and (loga *logb *logc)/6=6

find number of solution

• que was a b c r in gp and (loga +logb +logc)/log6=6
  
  a,b,c are in gp mean (b)^2=ac
  
  log(abc)/log6=6
  =>log(abc) base 6=6
  =>abc=(6)^6
  =>b^3=6^6 (since b^2=ac)
  =>b=36
  mean ac=36*36=2*2*3*3*2*2*3*3
  possible combination
  take a=1,b=36 ,c=36*36
  take a=2 ,b=36,c=36*18
  take a=3,b=36,c=36*12
  
  like that total soln =1+3*3 =10 ,you can check one one ,and keep in mind that abc should be in gp and in increasing order acc to question.
  
• 10 years agoHelpfull: Yes(3) No(1)
• log(a+ar+ar^2)=36
  a+ar+ar^2=10^36
  a(1+r+r^2)=10^36
  infinite solution are possible
  supose
  a = (10^36)/7, than r=2
  (10^36)/7 * 7 = 10^36
  so acc. to me infinite combination are there
• 10 years agoHelpfull: Yes(2) No(1)
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• Ques was abc are in GP and logalogblogclog66then we hav to find the possible combination of ab and csolif ab and c are in GP means b2acnowlogabclog66logb3log66logblog62b6236now b2ac ie 362acie ac6262 ie comb1ac9242 ie comb3ac12232 ie comb3ac18222 ie comb3ac3621 ie comb3ie total no of combination13
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