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HW problem

  1. Dec 21, 2004 #1

    01

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    Here's the question:

    Simplify the following as much as possible:

    ln 5th Sqrt of y^2

    a> 2/5 ln y

    b> -3 + ln y

    c> 3 + ln y

    d> 5/2 ln y

    A,B,C, or D, which is it?
     
    Last edited: Dec 21, 2004
  2. jcsd
  3. Dec 21, 2004 #2
    You can write the 5th sqrt of y^2 as y^(2/5) ....... knowing that, it should be easy to get the right answer
     
  4. Dec 21, 2004 #3

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    I'm wanting to say "A", correct?
     
  5. Dec 21, 2004 #4
    Yeap!

    ...........
     
  6. Dec 21, 2004 #5

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    Thanks for the input, now for another, I'm pretty sure of my answer I just want to be sure. Here it is:

    Solve the following equation

    log(base)5(x - 1) = -1

    a> 6

    b> 0.2

    c> 1.2

    d> 0.8

    My initial calculations (if they could be called that) came up with C, is that it?
     
  7. Dec 21, 2004 #6

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    Here's another while I'm at it:

    Suppose you have $6000, how much does a return of 3.25% compounded quarterly for 5 years yield?

    a> 6195

    b> 7040.47

    c> 6975

    d> 7054.06

    I'm wanting to say "B", but am unsure, any help?
     
  8. Dec 23, 2004 #7

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    ***bump***
     
  9. Dec 23, 2004 #8

    dextercioby

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    Homework Helper

    Well,it's right:
    [tex]5^{\log_{5}(x-1)}=5^{-1}\Rightarrow x-1=\frac{1}{5}\Rightarrow x=\frac{6}{5}=1.2 [/tex]

    Here's another while I'm at it:

    Suppose you have $6000, how much does a return of 3.25% compounded quarterly for 5 years yield?

    a> 6195

    b> 7040.47

    c> 6975

    d> 7054.06

    I'm wanting to say "B", but am unsure, any help?

    So the interest is 3.25% per quarter of the year (trimester)??It means 13% per year.That means 780$ per year,which is 3900$ per 5 yrs.

    If the interest is 3.25% per year,then it's 4 times less:975$ per 5 years,bringing it to a total of 6975$.Answer c).


    In this case,what the hell means "compounded quarterly"??Capitalization once every three months???In this case,the rate per trimester is 3,25%/4=0.8125%.For the first trimester it would be 48.75$.Then for the second semester it would be:6048,75$*0.8125%=49.14609375$.So the total for 6 months would be:6097,89609375$.And for the third semester it would be 6097,89609375$*0.8125%=49.5454057617...$(the calcuator gave me only 10 decimals instead of 14).And the procedure would go on.
    I don't know what the final result will be,but definitely it is weird.

    Daniel.
     
  10. Dec 23, 2004 #9
    This is how do it. Develope a simple equation.
    First Quarter: [tex] R1 = (6000 + \frac {0.8125}{100} 6000) = 6000(1+ \frac{0.8125}{100})[/tex]


    For the second Quarter: [tex] R2 = (R1 + \frac {0.8125}{100} R1) = R1(1+ \frac{0.8125}{100}) = 6000(1+ \frac{0.8125}{100})^2[/tex]

    There are 20 quarters in 5 years.
    So the return after 5 years R20, is given by

    [tex] R20 = 6000(1+ \frac{0.8125}{100})^{20}[/tex]


    This gives $ 7054.05 (d)


    Regards,

    Gamma.
     
  11. Dec 29, 2004 #10
    Another approach to this problem is to use the formula for changing the base, which is:

    Log(base x)N=(Log(base 10)N)/(Log(base 10)x).

    This can be very useful in any future quizzes or exams that you may have. This is also applicable for Ln (which is Log(base e)), e=2.7182...

    Applying this formula to your original problem, the equation would look like this:

    Log(base 5)(x-1)=-1
    (Log(base 10)(x-1))/(log(base 10)5)=-1

    Note: Log(base 10)=Log,
    futher simplifying, we get

    Log(x-1)=-1*Log5

    Using properies of logarithms, we get Log(x-1)=Log(5^-1),
    take the anti-logarithm of both sides we get, x-1=1/5

    therefore answer is: x=1+1/5 or 1.2 :wink:

    PS: Can someone help me with my thread (Supplementary angles for Spherical triangles)??
     
    Last edited: Dec 29, 2004
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