1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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:

    (log(subx)7)(log(sub7)5)=2
    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:

    [tex]\frac{\log_{5}}{2}=\log_{x}[/tex]
     
  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
    attachment.php?attachmentid=22535&stc=1&d=1260950590.jpg
     

    Attached Files:

    • 2.jpg
      2.jpg
      File size:
      5.6 KB
      Views:
      148
  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

    HallsofIvy

    User Avatar
    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
    "If
    [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

    Borek

    User Avatar

    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...
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook