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Proving vector space, associativity

  1. Feb 19, 2008 #1
    1. The problem statement, all variables and given/known data
    Im doing a problem where im trying to show that an abelian group with a scalar multiplication is a vector field. Im trying to show associativity right now and just have a question:

    im trying to show that exp(b.c.lnx) = b.exp(c.lnx)

    But im not very sure of my logs and exp's laws, not sure that they are even equal. Any pointers guys?


    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Feb 19, 2008 #2
    They wouldn't be equal.

    Since [tex]e^x[/tex] and [tex]\ln x[/tex] are inverses of each other, [tex]e^{\ln x} = x[/tex]. Therefore, your expressions can be simplified to [tex]x^{bc} = bx^c[/tex] which are not equal.

    Also, a simple counter-example shows the same result: Taking [tex]x=3, b=2, c=1[/tex] we have [tex]3^{1\cdot 2}=2\cdot 3^1[/tex] which is obviously not true.
     
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