Simplify log3(2)*log4(3)*log5(4)*log6(5)......*log20(19)

A.log2(20)
B.None of the above
C.log20(2+3+4+.....+19)
D.log20(2)

• D
  Apply the formula : log a(b) =log b/log a.
  Keep on applying the formula we will get :
  log 20(2).
• 5 years agoHelpfull: Yes(6) No(1)
• log a(b) = log b
  --------
  log a
  
  for example,
  
  log 3(2) = log 2
  -------
  log 3
  
  hence,
  log 2 log 3 log 4 log 19 log 2
  ------- * ------- * ------- .............................. --------- = --------- => log 20(2)
  log 3 log 4 log 5 log 20 log 20
• 5 years agoHelpfull: Yes(2) No(4)
• we can write the above expression as (log2/log3 )*(log3/log4).......(log19/log20)
  Now, we can infer from the above-deduced expression the denominator part of the successive expression is getting canceled. In the end, we are only left with log2 /log20 which can be written as log20(2)
• 5 years agoHelpfull: Yes(2) No(0)
• D
  since log b(a) = log a/ log b
  therefore on simplifying we get log 2/ log 20 i.e; log 20(2)
• 5 years agoHelpfull: Yes(1) No(0)
• log20/log2
• 5 years agoHelpfull: Yes(0) No(4)
• log a (b)=log b /log a
  log20(2)
• 5 years agoHelpfull: Yes(0) No(1)
• log a(b) = log b / log a
  
  for example,
  
  log 3(2) = log 2 / log 3
  
  hence,
  log 2 log 3 log 4 log 19 log 2
  ______* _______ * ______and so on....*_______==________ => log 20(2)
  log 3 log 4 log 5 log 20 log 20
• 5 years agoHelpfull: Yes(0) No(0)
• D.log20(2)
• 5 years agoHelpfull: Yes(0) No(0)
• All the terms will get cancelled
• 5 years agoHelpfull: Yes(0) No(1)
• Option D.log20(2)
  
  explanation:
  log2/log3.........*log19/log20 = log2/log20 = log20(2)
• 5 years agoHelpfull: Yes(0) No(0)
• log20(2)
  expand and divide each other
• 5 years agoHelpfull: Yes(0) No(0)
• A. log2(20)
• 5 years agoHelpfull: Yes(0) No(0)
• D.log20(2)
• 5 years agoHelpfull: Yes(0) No(0)
• C is the answer by
  log property of multipication..
• 5 years agoHelpfull: Yes(0) No(0)