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Math help please

  1. Dec 7, 2004 #1
    math help please!!

    here is the question i am having trouble with.

    5^(log(3X) – log(3)2) = 125...where the base is in brackets.

    This is how i attempted to solve for x, but i got stuck. Can someone please help me out. thanks

    I understand u can make the 125=5^3 and then:
    log(3X) - log(3)2 = 3
    log(3X) = 3 + [(log2)/(log3)]
    log(3X) = 3.63
    Now what? :uhh:

    The answer in the book is 54.
  2. jcsd
  3. Dec 7, 2004 #2


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    Exponentiate both terms of the last equation.Your answer would ly a mere division away.

  4. Dec 7, 2004 #3
    I'm assuming that log(3X) is actually log3x. Recall the definition of the logarithm, that logba = c means that bc = a and vice-versa.
  5. Dec 7, 2004 #4
    no 3x is the base
  6. Dec 7, 2004 #5
    i dont understand what you are trying to say here :redface:
  7. Dec 7, 2004 #6
    Then what are you taking the logarithm in base 3x of ?
    Ie. log3x4 = 12 would be a valid equation (read "the logarithm in base 3x of 4 is 12"), but log3x = 12 is a meaningless fragment.
  8. Dec 7, 2004 #7
    hmmm maybe its a typo in my book.
  9. Dec 7, 2004 #8
    Possibly. For the record, reading it as log3x does give x=54.
  10. Dec 7, 2004 #9
    yes that makes more sense
  11. Dec 7, 2004 #10
    thanks for ur help
  12. Dec 8, 2004 #11


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    I think the equation should be:

    log(3)x means logarithm of x with base 3.

    At this point you can solve brute force but you can do this without any calculator
    Hint: rewrite 3 as a log(3)something then the answer pops right out.
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