Who wants a math challenge?

majormattmajormatt
Posted:
in General Discussion edited January 2014
Solve this without any graphing calculators or technology (yes, I know the answer is ~ 4.48,) just algebraically.



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Comments

  • Reply 1 of 26
    scottscott Posts: 7,431member
    Isn't that what we call a transcendental equation?
  • Reply 2 of 26
    scottscott Posts: 7,431member
    No wait that's something else.
  • Reply 3 of 26
    scottscott Posts: 7,431member
    No wait I think I'm right.



    If we take log base 2 we get





    log_2(5) constant + log_2(x) = x





    So whenever that's true you know what X is. But that's true for the first one anyway.
  • Reply 4 of 26
    majormattmajormatt Posts: 1,077member
    That's as far as I practically got, too. Getting rid of the second x still remains elusive, it seems to go round about.
  • Reply 5 of 26
    aquafireaquafire Posts: 2,758member
    Scott.

    quote from " Forest Gump "

    " You must be a Goddam genius "

    I had it as X = X

    But your cleverererer than me
  • Reply 6 of 26
    scottscott Posts: 7,431member
    You should see how fast I can put a riffle together.
  • Reply 7 of 26
    majormattmajormatt Posts: 1,077member
    Not where I intended this thread to go...
  • Reply 8 of 26
    scottscott Posts: 7,431member
    Quote:

    Originally posted by MajorMatt

    Not where I intended this thread to go...



    So is there a solution other than the typical way of dealing with this. Which if I remember is to plot y=log_2(5) + log_2(x) and y=x and see where they cross.
  • Reply 9 of 26
    scottscott Posts: 7,431member
    Are there two answers?
  • Reply 10 of 26
    majormattmajormatt Posts: 1,077member
    There are two answers, which I forgot.



    Anyhow plotting is breaking the rules of this exercise.
  • Reply 11 of 26
    aquafireaquafire Posts: 2,758member
    MajorMatt,

    I can't stand the suspense. Two answers.

    Does that mean I am correct as well ?

    Are you holding out ?

    Byt the way

    What is the square root of Pi ?
  • Reply 12 of 26
    rick1138rick1138 Posts: 938member
    It's pretty damn difficult.





    I got it into the form:





    ln 5x = x ln2



    Then tried taking the derivative of each side, but it didn't work.
  • Reply 13 of 26
    cosmonutcosmonut Posts: 4,872member
    And this, my friends, is why I make a living with a video camera and an Avid.
  • Reply 14 of 26
    fangornfangorn Posts: 323member
    But what does it all MEAN?



    The answer to life and everything is 4!!!
  • Reply 15 of 26
    rick1138rick1138 Posts: 938member
    Square root of pi is 1.7724538509
  • Reply 16 of 26
    paulpaul Posts: 5,278member
    Ti 89s rock:

    Solve(2x=5x,x)

    x=4.48800113601 or x=.235455710071
  • Reply 17 of 26
    rick1138rick1138 Posts: 938member
    I don't see a way to do it symbolically, it might not be solvable. Logarithms can be decomposed intoe series, but the series themselves are unsolvable, because they contain quintic and above polynomials - the best way is to use an approximation.





    4.488

    0.235
  • Reply 18 of 26
    aquafireaquafire Posts: 2,758member
    seeing these answers makes me realise why there is no " numbers noodle soup" to match the

    "alphabet noodles in my soup"

    Shows how deeply ingrained is our fear of bogey man maths.\
  • Reply 19 of 26
    cyclecycle Posts: 187member
    actually its pretty easy (someone had to say this...)



    take for example 3^X=9X



    the answer is 2



    so...2^X=4X



    2? yes



    its a reduced equation..alright...and its a (n=x) root backwards



    and this one is the irritating part:



    root from 5=2.236...x2=4.472...



    the evil number 2 is messing with ur head



    4.488001136
  • Reply 20 of 26
    rick1138rick1138 Posts: 938member
    No it's not easy at all - all of your calculations are incorrect.
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