A Logarithm Question

• Ahm97sic

  30 Sep 08, 00:36

  This question is fun. Perhaps you will like to solve it.

  Question

  Given that log3[log2(log5 a)] = log5[log3(log2 b)] = log5[log2(log3 c)],

  Find the value of a + b + c. 

  [The number in red is in subscript ie the base of the log].

  Thank you for your kind attention.

  Regards.

  ahm97sic

• ^tamago^

  30 Sep 08, 00:39

  lai lai help u display the equation. (:
  
  

• Ahm97sic

  30 Sep 08, 00:42

  Hi Tamago,

  Thanks for helping to type the mathematical symbols in the forum.

  Thank you for your kind attention.

  Regards,

  ahm97sic

• Ahm97sic

  1 Oct 08, 10:34

  Question

  Given that

  Find the value of a + b + c

   

• secretliker

  2 Oct 08, 23:16

  Hmm from the equation, the first thing I could see is that:

  log3 (log2 b) = log2 (log3 c)

  Or is it equal?

  No idea on what to do next.

• donkhead333

  3 Oct 08, 17:27

  log5(log3(log2b)) = log5(log2(log3c))

  log5[(log3(log2b))/(log2(log3c))] = 0

  [(log3(log2b))/(log2(log3c))] = 1

  (log3(log2b)) = (log2(log3c))

  (log2(log2b)/log2(3)) = log2(log3c)

  log2(log2b) = [log2(log3c)](log2(3))

  no idea on what to do next..

  wonder if there's any error in my working?

   

   

• Ahm97sic

  3 Oct 08, 19:44

  Hi Secret Killer and Donkhead333,

  This question looks complicated and difficult but actually it is not difficult or complicated once you discover the trick or the fun part of the question.

  I do not know how to type mathemtical symbols eg log 5 a in the forum.

  I have typed out the answer using Mathtype in Microsoft Word 2003. I can send you an email with the answer in the attached file. 

  Thank you for your kind attention.

  Regards,

  ahm97sic

• Ahm97sic

  4 Oct 08, 11:07

  Hi Donkhead333,

  The first part is on the correct path to the answer but the second part has gone off the path. Keep trying and you are sure to get the answer. Don't think it to be difficult, the answer is actually quite simple once you discover the trick or the fun part of the question.

  This question appears to be complicated and difficult but actually it is quite simple once you found the answer ie the fun part of the question.

  Thank you for your kind attention.

  Regards,

  ahm97sic

• Ahm97sic

  4 Oct 08, 11:35

  Hi Secretkiller and Donkhead333,

  Oops, I just realized that I have forgotten to type equal zero for the question ie

  Question

  Given that log3[log2(log5 a)] = log5[log3(log2 b)] = log5[log2(log3 c)] = 0,

  Find the value of a + b + c. 

  [The number in red is in subscript ie the base of the log].

  Please accept my apologies.

  The answer of a + b + c = 42.

  Thank you for your kind attention,

  Regards,

  ahm97sic

• FirePig

  4 Oct 08, 11:38

  log3[log2(log5 a)] = log5[log3(log2 b)] = log5[log2(log3 c)] = 0,

  log3[log2(log5 a)] =0

  [log2(log5 a)] =3^0 = 1

  (log5 a) = 2^1 = 2

  a = 5^2 = 25

  Same for the rest

• dadeadman1337

  4 Oct 08, 11:53

  Wah liu, got the zero then damn easy

• FirePig

  4 Oct 08, 12:08

  Without the zero, there will be infinitely many answers. Just let the equation be = 1, then = 2, then =3 and so on. 

• skythewood

  4 Oct 08, 12:21

  instead of 0, let it be x

   

  log3[log2(log5 a)] =x

  [log2(log5 a)] =3^x 

  (log5 a) = 2^3^x

   

  a = 5^2^3^x

  b = 2^3^5^x

  c = 3^2^5^x

   

  just sub in any x you like,

  a + b + c = the answer you want.

   

   

• eagle

  4 Oct 08, 12:46

  Originally posted by skythewood:

  instead of 0, let it be x

   

  log3[log2(log5 a)] =x

  [log2(log5 a)] =3^x 

  (log5 a) = 2^3^x

   

  a = 5^2^3^x

  b = 2^3^5^x

  c = 3^2^5^x

   

  just sub in any x you like,

  a + b + c = the answer you want.

   

   

  very well done