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Math Help - 3^y > y^3

  1. #1
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    3^y > y^3

    Does anyone know how to solve this: 3^y > y^3

    I am pretty sure it's y> 3 but i cant prove it.
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  2. #2
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    Quote Originally Posted by fivosk7 View Post
    Does anyone know how to solve this: 3^y > y^3

    I am pretty sure it's y> 3 but i cant prove it.

    The graph of 3^y - y^3 shows that the only interval where y^3>3^y is between somewhere near y=2.5 and y=3. It's obvious that the two functions 3^y and y^3 are equal when y=3. The only way I can see to show that 3^y > y^3 when y>3 is to use calculus (which I guess isn't allowed in the pre-calculus forum). To find the other point where the two functions are equal is definitely tricky – there is no elementary way to find the point where the graph crosses the axis near y=2.5.
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