log3 N+log9 N what is 3 digit number N that will be whole number

• No of values N can take is 1
  9^3=729
• 9 years agoHelpfull: Yes(9) No(1)
• 729 was not an option
• 9 years agoHelpfull: Yes(3) No(0)
• 3log N base 9=whole number when N=9,81,729,6561
  so ans will 729
  
• 9 years agoHelpfull: Yes(2) No(0)
• log3N+1/2log3N=odd
  log3N()1+1/2)=odd
  log3N(3/2)=odd
  N=243 or 728
  but only 729 is satisfying
  so N=729
• 9 years agoHelpfull: Yes(1) No(1)
• 729 will be the answer
  
• 9 years agoHelpfull: Yes(0) No(0)
• BREIFly explain please
• 9 years agoHelpfull: Yes(0) No(0)
•  36=729
   93=729
   log3729+log9729
   log336+log993
   6log33+3log99
   9
  
• 9 years agoHelpfull: Yes(0) No(0)
• log3N + log3N/log 9 base 3 [ using base change property]
  log3N + log3N - log 9 base 3
  2log3N = log 9 base 3
  log 3 N^2 = log 9 base 3
  N^2 = 9 [ log cancelled out]
• 7 years agoHelpfull: Yes(0) No(1)