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Log equations help!

  1. Nov 26, 2012 #1
    1. The problem statement, all variables and given/known data

    Solve for x

    logbase 4 for question 1.

    1. log (x+2) - log (x-4) =1/2

    log base 2:

    2. log (3x+1) = 2 - log (x-1)

    log base 10:

    3. log sq root (x^2 -21x) =1

    similar just different numbers..

    log (x-4) - log (x+2) =4 base 2
    log (x-4)=4-log(x+2)
    log (x^2-2x)^7=21


    2. Relevant equations
    Log laws

    3. The attempt at a solution

    1. log (x+2)/(x-4) = 1/2 - is that right or is it log (x+2) = 1/2 + log (x-4) then cancel the logs. I dont know. When i tried it both didnt work. Maybe i calculated it wrong if its set up right.
    2. (3x+1)(x-1) = 2
    3x^2-2x-1=2
    3x^2-2x-3 - what do i do from here?

    3. If you square both sides, or times the square and x by .5 and equal it to zero, i dont know what to do, same process of solving for the later 3 im pretty sure im having difficulty with these.

    Any help please
     
  2. jcsd
  3. Nov 27, 2012 #2
    1. log (x+2)/(x-4) = 1/2 looks fine. Next step: get rid of the log.

    2. (3x+1)(x-1) = 2 -- Here you did just that, i.e. got rid of the log, but only on the left side. You need to fix the right side before you work out (3x+1)(x-1)

    3. log( √ something ) = something else ... get rid of the log first:
    √ something = 10 ^ (something else) ... square each side:
    something = (10 ^ (something else)) ^ 2 = 10 ^ (2 times something else)
    This is a quadratic equation which you should be able to solve. (Hint: the number 29 should appear somewhere on the way. If you see that, you're probably getting on okay.)
     
  4. Nov 27, 2012 #3

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Are you clear on what a logarithm is? It is the inverse to the exponential function- if y= loga(x), then x= ay. So if log4 A= 1/2, then 1/2= 4A. What A makes that true?
     
  5. Nov 27, 2012 #4
    Try again.
     
  6. Nov 27, 2012 #5
    If log4 A = 1/2, then A = 41/2...
     
  7. Nov 27, 2012 #6

    HallsofIvy

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    Staff Emeritus
    Science Advisor

  8. Nov 28, 2012 #7

    Mark44

    Staff: Mentor

    We all have our days ...
     
  9. Nov 28, 2012 #8
    i got them all ha it was just simple as getting rid of the log, silly we all do have our days.. thank to all of you though
     
  10. Nov 28, 2012 #9
    Halls seems to have her bad days more often than not!
     
  11. Nov 28, 2012 #10

    Mark44

    Staff: Mentor

    I would disagree on two points:
    1. I have rarely seen him make a mistake.
    2. Halls is a "he".
     
  12. Nov 28, 2012 #11
    Ok, I would disagree on just the one point. For some reason, I thought HoI was a she.

    But I haven't got enough fingers on both hands to count how many errors he's made in the last month or two! (Ok, maybe that's a bit harsh, but for a "PF MENTOR", far more than enough.)
     
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