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Math Help - exponent equation

  1. #1
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    exponent equation

    Just a simple question. How do we find R if it is given by the equation

    [(100-R)^0.5]+[(400-R)^0.5]=20

    I have tried taking the natural logs on both sides of the equation, but it does not return the correct answer, which is 93.75.

    Many thanks in advance.
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  2. #2
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    Quote Originally Posted by kenobings View Post
    Just a simple question. How do we find R if it is given by the equation

    [(100-R)^0.5]+[(400-R)^0.5]=20

    I have tried taking the natural logs on both sides of the equation, but it does not return the correct answer, which is 93.75.

    Many thanks in advance.
    Hello,

    to get rid of the square roots you must square both sides:

    [(100-R)^0.5]+[(400-R)^0.5]=20

    100-R + 2(100-R)^0.5*(400-R)^0.5 + 400-R = 400

    (100-R)^0.5*(400-R)^0.5 = R - 50 Square again:

    (100-R)(400-R) = Rē - 100R + 2500

    40.000 - 500R + Rē = Rē - 100R + 2500

    37.500 = 400R ==> R = 93.75
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  3. #3
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    thanks very much for the help.. any idea why taking natural logs on both sides wouldn't work?
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by kenobings View Post
    thanks very much for the help.. any idea why taking natural logs on both sides wouldn't work?
    we do not know how to evaluate log(x + y) unless we know exactly how to combine x and y into one number, which in this case we don't. also, taking logs is more trouble than it's worth here, since if we decide to separate the bases so we can take logs, we would have different bases, so we'd end up simplifying one and leaving (or possibly complicating) the other base

    note, here your bases are (100-R) and (400-R)
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