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Math Help - Simplify

  1. #1
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    Simplify

    (1/5)^3y=0.008 then (0.025)^y will be
    (a)0.25
    (b)0.0625
    (c)0.125
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by devi View Post
    (1/5)^3y=0.008 then (0.025)^y will be
    (a)0.25
    (b)0.0625
    (c)0.125
    solve for y in the first equation, and then plug in its value into the second to find its value

    can you solve for y?
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  3. #3
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by Jhevon View Post
    solve for y in the first equation, and then plug in its value into the second to find its value

    can you solve for y?
    If that is the correct equation, then the answer wouldn't match any of the choices...

    --Chris
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  4. #4
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    Quote Originally Posted by Chris L T521 View Post
    If that is the correct equation, then the answer wouldn't match any of the choices...

    --Chris
    Perhaps (a) should've been 0.025
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  5. #5
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    Quote Originally Posted by Chris L T521 View Post
    If that is the correct equation, then the answer wouldn't match any of the choices...

    --Chris
    The answer is given as 0.25
    It is whole power 3y
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  6. #6
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    Given: (\frac{1}{5})^{3y}=0.008

    Take the log (unspecified base, but same base on both sides.) of both sides: \log{(\frac{1}{5})^{3y}} = \log{0.008}

    Carry down 3y: 3y \cdot \log{\frac{1}{5}} = \log{0.008}

    Divide by 3 and \log{\frac{1}{5}} on both sides: y = \frac{\log{0.008}}{3 \cdot \log{\frac{1}{5}}}

    y = ...
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  7. #7
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by devi View Post
    (1/5)^3y=0.008 then (0.025)^y will be
    (a)0.25
    (b)0.0625
    (c)0.125
    Well, \tfrac{1}{5}^{3y}=.008\implies \tfrac{1}{125}^y=.008

    However, .008=\tfrac{1}{125}, so we get the expression \tfrac{1}{125}^y=\tfrac{1}{125}

    The only value of y that causes this expression to be true is y=1

    But then (0.025)^y\implies(0.025)^1=0.025...

    However, this isn't one of the solutions...

    --Chris
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  8. #8
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Chris L T521 View Post
    Well, \tfrac{1}{5}^{3y}=.008\implies \tfrac{1}{125}^y=.008

    However, .008=\tfrac{1}{125}, so we get the expression \tfrac{1}{125}^y=\tfrac{1}{125}

    The only value of y that causes this expression to be true is y=1

    But then (0.025)^y\implies(0.025)^1=0.025...

    However, this isn't one of the solutions...

    --Chris
    i concur. the final answer is 0.025
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  9. #9
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    Quote Originally Posted by devi View Post
    (1/5)^3y=0.008 then (0.025)^y will be
    (a)0.25
    (b)0.0625
    (c)0.125
    Solution:

    (1/5)^3y= 0.008
    (1/5)^3y = (0.2)^3
    (0.2)^3y = (0.2)^3
    y=1

    Now
    (0.025)^y
    = (0.025)^1
    =0.025
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