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owlet

  • one year ago

Find the intersection of \(x^3\) and \(3^x\) How to do it?

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  1. zzr0ck3r
    • one year ago
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    Hint for one solution: \(a^a=a^a\). The other solution gets a little tricky. Google "analytic continuation of the product log function"

  2. owlet
    • one year ago
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    so x=3? one point of intersection would be (3, 27) ?

  3. zzr0ck3r
    • one year ago
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    Are you asking me if 3^3 = 27?

  4. owlet
    • one year ago
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    no, if one of the intersection points of these two function would be (3, 27)

  5. owlet
    • one year ago
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    how about the other point?

  6. zzr0ck3r
    • one year ago
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    put in \(x=3\) on both functions, and then see what you get out...

  7. zzr0ck3r
    • one year ago
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    As far as the other point, I refer you to my first comment.

  8. zzr0ck3r
    • one year ago
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    The solution is transcendental, so like \(\pi\) there is no good way to explain it with numbers :)

  9. owlet
    • one year ago
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    oh got it. thanks.. no point of solving this thing because its too complicatedlol but I understand the first solution though :) tysm

  10. zzr0ck3r
    • one year ago
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    yeah, it is crazy. There actually might be infinite solutions, but only one is algebraic, meaning we can express it with numbers and symbols...

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