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Logarithms i need help.

  1. May 12, 2004 #1
    Logarithms....i need help.

    A logarithm of a number is the exponent of the power to which a fixed number. called the base, must be raised to produce the given number.

    I absolutely do not understand what these things mean. In my text book it shows a graph of x=10y.
    Then it follows with 6 questions which are as follows:
    1. For what values of x do the corresponding logarithms change most rapidly?
    2. How does the rate of change of y compare with that of x for values of x between 1 and 10?
    3. For what values of x are the values of y negative?
    4. What is the approximate value of y when x=8? 15? 28?
    5. What is the number whose logarithm is .2? .4? 1.2? 1.4?
    6. Show that in the graph log 10 is approximately equal to log 5+log 2; that log 5 is approximately equal to log 25-log 5. that log 27 is approximately equal to 3 log 3.

    PLEASE ANSWER BUT EXPLAIN HOW THESE ARE DONE PLEASE......

    Thanks.
    :wink: Amber :wink:
     
  2. jcsd
  3. May 12, 2004 #2

    Janus

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    I won't answer your questions for you, but I will try to explain logarithms so that you will understand them well enough to do them yourself.

    If you take the equation

    [tex]10^{2}=100[/tex]

    Ten is the base, and 2 is the exponent.

    A logarithm is basically solving for x in the following:

    [tex]10^{x}=100[/tex]

    here x = 2

    for

    [tex]10^{x}= 1000[/tex]

    x=3

    Another way of writing this would be

    [tex]log_{10}1000 = 3[/tex]

    Which would read "The log of 1000, base 10, is 3"

    The general form of this equation is

    [tex]log_{base}(number) = exponent[/tex]

    The exponent (or log of the number) does not have to be a whole number.

    Thus, the log of 5, base 10 would be 0.69897 or

    [tex]log_{10}5 = 0.69897[/tex]

    or of 15:

    [tex]log_{10}15 = 1.1761[/tex]

    Hope this helps
     
  4. May 12, 2004 #3

    jcsd

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    As your only worried about base 10 logarithms:

    [tex]10^{log(x)} = x[/tex]

    The above equation all you really need to know for now.

    I assume that the graph in the book isn't x = 10y, but x = 10y, so just by looking at the above equation you should be able to see that y = log(x).
     
  5. May 13, 2004 #4

    arildno

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    This phrase seems meaningless to me as well!.
    I would have said:
    A logarithm (with respect to a number B) of a number A is the power to which B must be raised in order to produce A.
    The power to which we raise a number is often called the exponent;
    the number to be raised is called the base.
    If the base is B, the exponent that produces A is called the B-logarithm to A.

    Read the other replies carefully; these detail the procedure needed to solve the problems.
     
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