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Homework Help: Log sums

  1. Jul 19, 2010 #1
    1. The problem statement, all variables and given/known data
    I have 2 problems ,which are:
    1) Solve :log 7 (x 3+27) + log 7 (x+3)
    2) Solve for x:log5 ( 5 1/x+ 125) log 5 6+1+1/2x

    2. Relevant equations

    3. The attempt at a solution
    The first one tried like this :
    log 7 { (x 3+27)/(x+3) }= 2
    or 7 2 = (x 3+27)/(x+3)
    But I don't know how to proceed beyond it please help!
    in second one
    log5{( 5 1/x+ 125) /6}=1+1/2x
    but I can't proceed here too.
    I need an urgent help!
    Thank You!
  2. jcsd
  3. Jul 19, 2010 #2


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    Homework Helper

    Please check the original problems as I see typos abound. For instance, in the first problem,

    log 7 (x 3+27) + log 7 (x+3)

    ...I see no right hand side. Also, if what you have above is correct, then you're next step...

    log 7 { (x 3+27)/(x+3) }= 2

    ...is already wrong. (Is is supposed to be divide?)

    Finally, if the last step above is supposed to have a divide, then review factoring special products -- specifically, the sum of two cubes.

  4. Jul 19, 2010 #3


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    Homework Helper

    For the first one, you could multiply through by x+3 to give


    and then solve that cubic by simplifying and turning it into the form [tex]ax^3+bx^2+cx+d=0[/tex]
    but cubics are hard to solve, an easier way would be to realize that [tex]x^3+27[/tex] is a sum of two cubes, mainly [tex]x^3+3^3=(x+3)(x^2-3x+9)[/tex] which means you can cancel the x+3 from the numerator and denominator, giving you only a quadratic to solve, which is much simpler. Remember to look back at the original question to figure out what the domain of x is.

    For the second, do the same thing as you did above, turn the log into powers such that


    Now simplify the right hand side. You should be able to factorize out 51/x and then solve.
  5. Jul 20, 2010 #4
    I agree with eumyang. Is the question to simply the above expressions? Also, with the second problem, are you missing any brackets/parenthesis at all?

    The Bob
  6. Jul 21, 2010 #5


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    Science Advisor

    At least in the second, 1/2" specifically says "solve for x". There are no equations to be solved!
  7. Jul 21, 2010 #6


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    Homework Helper

    It's an honest mistake to mix up + and = considering they're the same key on the keyboard, but he did have lots of typos so it could have been re-interpreted as anything.

    And for the first equation, let's just assume he started to solve the correct problem, i.e. f(x)=2.
  8. Jul 23, 2010 #7
    Thanks for the help but I figured it out!
    Thanks everyone!
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