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Exponential and logarthmic functions

  1. Jan 12, 2012 #1
    1. i) For what values of a with the expression log2a:

    a) yield positive numbers?
    b) yield negative numbers?
    c) yield numbers greater than 1?
    d) yield numbers between 0 and 1?
    e) be zero?
    f) be undefined?


    Solution:

    1. a) a > 1
    b) 0 < a < 1
    c) ?
    d) ?
    e) a = 1
    f) a < 0
     
  2. jcsd
  3. Jan 12, 2012 #2

    Mark44

    Staff: Mentor

    a, b, e, and f look fine.
    For the other two, it would be helpful to sketch the graph of y = log2x.
    (c) For what values of x is y > 1?
    (d) For what values of x is y between 0 and 1 (i.e., 0 < y < 1)?
     
  4. Jan 13, 2012 #3

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    [itex]y= log_2(x)[/itex] is the same as [itex]x= 2^y[/itex].
    c) when is [itex]log_2(x)< 0[/itex]?
    If y< 0 what is [itex]2^y[/itex]

    d) when is [itex]log_2(x)> 0[/itex]?
    If y> 0 what is [itex]2^y[/itex]?
     
    Last edited by a moderator: Jan 13, 2012
  5. Jan 13, 2012 #4

    Redbelly98

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    To the OP: your answer to (e) could help you with answering (c).
     
    Last edited by a moderator: Jan 13, 2012
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