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Logarithmic Equations

  1. Oct 1, 2008 #1
    I'm having a lot of trouble on this worksheet I have, I've got most of the 32 questions except for about 5. I won't type out all the laws of logarithms as I assume that anyone coming in here to help me already knows them. So here are my questions (By the way, I've done work for them I just won't show it because it seems like I'm stuck where I'm at regardless):

    17.) Solve for x:
    [tex](logx)^{logx}-9=0[/tex]

    24.) Solve for x, accurate to 2 decimal places
    [tex]log_{4}x+log_{5}x=8.7[/tex]

    26.) Simplify completely.
    [tex]\frac{log_{a}x}{log_{ab}x}-\frac{log_{a}x}{log_{b}x}[/tex]

    32.) Simplify/solve for x.
    [tex]ln^{2}x+lnx^{3}+2=0[/tex]

    33.) Simplify/solve for x.
    [tex]\frac{e^{x}+e^{-x}}{2}=k[/tex]

    Thank you for the help, I'm sorry about asking so many questions I just am really struggling on this one.
     
  2. jcsd
  3. Oct 1, 2008 #2
    Ok I did 26 and got this:

    [tex]\frac{log_{a}x}{log_{ab}x}-\frac{log_{a}x}{log_{b}x}[/tex]

    [tex]\frac{logx}{loga}(\frac{logab}{logx})-\frac{logx}{loga}(\frac{logb}{logx})[/tex]

    [tex]\frac{logab}{loga} - \frac{logb}{loga}[/tex]

    [tex]log_{a}ab - log_{a}b[/tex]

    [tex]log_{a}\frac{ab}{b}[/tex]

    [tex]log_{a}a[/tex]

    = 1

    So I think I got 26, is that right?
     
  4. Oct 2, 2008 #3

    statdad

    User Avatar
    Homework Helper

    I haven't checked your calculations, but that is the right approach. You can use the same idea to solve 24 (convert the logs to the same base)

    With a judicious use of a another logarithm rule you can convert 32 to a quadratic equation in [tex] \ln x [/tex]

    Multiplication by a correctly chosen exponential function (and clearing the fraction by multiplying everything by 2) will convert the final one to a quadratic equation in [tex] e^x [/tex]
     
  5. Oct 2, 2008 #4
    Ok thank you, I have figured them all out now so it's good.
     
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