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Logarithms table help

  1. Nov 15, 2005 #1
    Hello there, Im wondering if you could offer some help on this questoin, I have been attempting to work through it, however cannot see exactly what route I should be taking to try and solve it;
    Without using a calculator or table, show that;
    2 < log(3) 25 < 3 (log to the base 3 of 25)
    and hence find the ceiling of log(3) 75
    Also calculate log(5) 75 in terms of log(3)5
    Thankyou for any help you can provide.
    Craig :)

    Edit:

    Sorry i forgot to mention, what i have done so far is;

    Shown that 3^3 = 27 and 3^2 = 9, this is simply setting log(3)x = 3 and 2 and i get a values in which 25 lies in

    9 < 25 < 27
     
    Last edited: Nov 15, 2005
  2. jcsd
  3. Nov 15, 2005 #2
    My logarithm knowledge is kind of sketchy but I think this is right:

    [tex]x = log_3 25[/tex]

    [tex]3^x = 25[/tex]

    If x were 3 then RHS would be 27, if it were 2 then RHS would be 9, since 25 is between these values then so is x.

    Q2:

    I think there is a rule that goes something like this (someone please confirm):

    [tex]log_x y = \frac{log_a y}{log_a x}[/tex] (where a can be anything you like).

    So

    [tex]log_5 75 = \frac{log_3 75}{log_3 5}[/tex]
     
    Last edited: Nov 15, 2005
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