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Homework Help: Simplifying logs

  1. Dec 16, 2009 #1
    1. The problem statement, all variables and given/known data
    How do i solve for the subscript in:
    (log (sub5)) / 2 = log(sub x)

    2. Relevant equations


    3. The attempt at a solution

    the original question was:

    solve for x.
    however i dont get how to solve for a subscript....
  2. jcsd
  3. Dec 16, 2009 #2
    i don't get your question:

  4. Dec 16, 2009 #3
    thats the right equation, i was just wondering if anyone could help me solve for that 'x'?
  5. Dec 16, 2009 #4

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  6. Dec 16, 2009 #5
    thank you so much, you make understanding logs really easy! thanks.
  7. Dec 16, 2009 #6
    Its my pleasure (=
  8. Dec 16, 2009 #7


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    Science Advisor

    Warning, shocklightnin. Icystrike may have misunderstood your question and given a wrong answer!

    I would interpret your question, since you specifically stated that "5" and "x" were "subscripts" (I would say "bases") as
    [tex]\frac{log_5(a)}{2}= log_x(a)[/tex]
    for some a, what is x?"

    Then icystrike is answering a completely different question:
    [tex]\frac{log(5)}{log(2)}= log(x)[/tex]
    which is, in a sense, the "reverse" of the original question!

    If my interpretion is correct, since [itex]log_x(a)= log(a)/log(x)[/itex] and [itex]log_5(a)= log(a)/log(5)[/itex], where "log" on the right of each equation can be to any base, it follows that
    [tex]\frac{log(a)}{log(5)}= 2\frac{log(a)}{log(x)}[/tex]
    Now the "log(a)" terms cancel out and we have

    [tex]\frac{1}{log(5)}= \frac{2}{log(x)}[/tex]

    That is the equation you want to solve.
  9. Dec 16, 2009 #8
    there was a missing "a" to the equation , thus , i check with him if he was referring to the above equation that i mention. Hope he will reply (=
  10. Dec 16, 2009 #9


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    Staff: Mentor

    Which seems to be

    [tex]\log_x 7 \times \log_7 5 = 2[/tex]

    and as far as I can tell it was not yet mentioned...
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