how many possible solution for (log a +log b
+log c)/(log 6)= 6? ( take log to the base 10)

• log a + log b +log c = log abc
  we need to find log abc/log 6
  => log (base6)abc = 6
  => 6^6 = abc
  =>3x3x3x3x3x3x2x2x2x2x2x2x1 = abc
  now its a combination problem
  'a' can be chosen in 7x7 ways
  i.e (0 threes or 1 three or 2 threes ....or 6 threes)AND(0 two or 1 two or 2 twos... 6 twos)
  then after 'b' can be chosen in (7x7)-1 [ ie same thing that is chosen as 'a' cannot be chosen as 'b']
  when 'a' and 'b' are chosen 'c' can only be one thing [i.e all remaining numbers multiplied]
  so its 49x48 ways = 2352
  
• 8 years agoHelpfull: Yes(9) No(7)
• question was how many possible solutions for (log a +log b
  +log c)/(log 6)= 6? If abc are in G.P
  
  soln :- log abc / (log 6)= 6
  
  take a = a
  b= ar
  c= ar^2
  then log base 6 abc = 6
  abc =6^6
  then (ar)^3=6^6
  ar=36
  ar= 2^2 * 3^2
  factors of 36 will be 9
• 8 years agoHelpfull: Yes(4) No(0)
• log6(abc)=6
  log6abc=log666
  abc=6^6
  possible cases=
  a=6^6 b=1 c=1 3 soln
  a=6^5 b=6 c=1 3 soln
  a=6^4 b=6^2 c=1 3 soln
  a=6^4 b=6 c=6 3 soln
  a=6^3 b=6^3 c=1 3 soln
  a=6^3 b=6^2 c=1 3 soln
  a=6^2 b=6^2 c=6^2 1 soln
  total 19 soln
  
• 8 years agoHelpfull: Yes(2) No(1)
• log(A*B*C) = 6*log 6 then log(A*B*C) = log(6^6)
  
  so A*B*C = 6*6*6*6*6*6
  so no of possibilities are
  (6*6,6*6,6*6) = 1
  (6*6*6,6*6,6) = 6
  (6*6*6*6,6,6) = 3
  so total 10 ways i think
• 7 years agoHelpfull: Yes(1) No(1)