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Math Help - Simplification :)

  1. #1
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    Simplification :)

    Hello
    I'm having trouble solving this daily interest rate conversion. I know the sollution because Maple does it for me but i cant get to it myself which drives me nuts. heres what i have so far
    1.07 = (1+R)^365
    ln 1.07 = 365 ln (1+R)
    ln1.07/365 = ln (1+R)
    now how do i get rid of the ln on the right?
    thank you, chris
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  2. #2
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    ln(1.07)/365 = ln (1+R)

    e^(ln(1.07)/365) = e^(ln (1+R))

    e^(ln(1.07)/365) = 1+R

    finish him off.
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  3. #3
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    Quote Originally Posted by ffezz View Post
    1.07 = (1+R)^365
    RULE: if a^p = b then a = b^(1/p)

    So 1 + R = 1.07^(1/365)
    Last edited by Wilmer; April 20th 2011 at 06:14 PM. Reason: add power sign!
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  4. #4
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    Quote Originally Posted by Wilmer View Post
    RULE: if a^p = b then a = b(1/p)

    Or maybe if a^p = b then a = b^(1/p)?
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  5. #5
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    Quote Originally Posted by ffezz View Post
    Hello
    I'm having trouble solving this daily interest rate conversion. I know the sollution because Maple does it for me but i cant get to it myself which drives me nuts. heres what i have so far
    1.07 = (1+R)^365
    ln 1.07 = 365 ln (1+R)
    ln1.07/365 = ln (1+R)
    now how do i get rid of the ln on the right?
    thank you, chris
    You only use logarithms to solve for exponents. In this case, to undo a power, take both sides to the reciprocal power.
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  6. #6
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    Haha thanks guys I got both methods. Now i remember how to use e^x and can also convert between interst rates without doing complicated algebra with the oh so neat reciprocal rule that i did not remember
    thank you
    Chris
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  7. #7
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    Quote Originally Posted by pickslides View Post
    finish him off.
    I like this.
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  8. #8
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    Quote Originally Posted by Wilmer View Post
    RULE: if a^p = b then a = b^(1/p)

    So 1 + R = 1.07^(1/365)

    I think it's supposed to be 1 + R = 1.07 / 365 right? Since you raised both sides to the exp it cancels out the ln.
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  9. #9
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    Absolutely not.

    (1 + R)^365 = 1.07

    [(1 + R)^365]^(1/365) = (1.07)^(1/365)

    1 + R = (1.07)^(1/365).
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  10. #10
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    Quote Originally Posted by Prove It View Post
    Absolutely not.

    (1 + R)^365 = 1.07

    [(1 + R)^365]^(1/365) = (1.07)^(1/365)

    1 + R = (1.07)^(1/365).

    My mistake. Thank you for clarifying.
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