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Solve for x

  1. Nov 25, 2014 #1
    1. The problem statement, all variables and given/known data
    [itex]81^5>32^x[/itex]
    Find the maximum value of [itex]x[/itex] in order to satisfy the inequality.

    2. Relevant equations
    Inequalities, indices

    3. The attempt at a solution
    Try to make the bases on both sides of the inequality same.
     
  2. jcsd
  3. Nov 25, 2014 #2

    ShayanJ

    User Avatar
    Gold Member

    You can't make the bases equal because [itex] 81=3^4 [/itex] and [itex] 32=2^5 [/itex]. You should solve [itex] 81^5=32^x [/itex] for x. That'll be the maximum value! Just get the logarithm(in any base) of both sides. That'll get out x in a way that you can isolate it.
     
  4. Nov 25, 2014 #3

    Mark44

    Staff: Mentor

    Actually, you can make the bases equal.
    815 = (34)5 = 320, and ##32 = 3^{log_3(32)}##
    To the OP:
    In future posts, you need to make more of an effort than this.
     
  5. Nov 25, 2014 #4
    You can reduce it somewhat:

    ##81^5 > 32^x = 2^{5x}##
    ∴ ...
     
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