Results 1 to 4 of 4

Math Help - Logs

  1. #1
    Member
    Joined
    Dec 2007
    Posts
    76

    Logs

    simplify using logarithm properties
    a)4log(subscript25)15-4log(25)3

    Express the following as a single logarithm
    c)1/3(log(5)X+log(5)Y)-4log(5)Z

    Simplify
    d)log(2)20-log(2)5

    thank you
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member wingless's Avatar
    Joined
    Dec 2007
    From
    Istanbul
    Posts
    585
    A summary of the basic properties:

    1- \text{log}_{c}a + \text{log}_{c}b = \text{log}_{c}ab


    2- \text{log}_{c}a - \text{log}_{c}b = \text{log}_{c}(\frac{a}{b})


    3- log_{a}{b} = \frac{\text{log}_{c}{b}}{\text{log}_{c}{a}} (c can be anything you want, don't forget that c > 0 and c \neq 1)


    4- a \text{log}_{b}c = \text{log}_{b}(c^a)


    5- \frac{1}{a}\text{log}_{b}c = \text{log}_{(b^a)}c


    Last two properties combined:
    6- \frac{c}{d}\text{log}_{a}{b} = \text{log}_{(a^d)}{(b^c)}


    7-Let's say that x = \text{log}_{a}{b}
    If I multiply it by \frac{c}{c}
    x = \text{log}_{a}{b} = \frac{c}{c}\text{log}_{a}{b}
    From property 6,
    x = \text{log}_{(a^c)}{(b^c)}
    Which means,
    \text{log}_{a}{b} = \text{log}_{(a^2)}{(b^2)} = \text{log}_{(a^3)}{(b^3)} = \text{log}_{(a^4)}{(b^4)} = \text{log}_{(a^{1/2})}{(b^{1/2})}....



    ---------------------------
    ---------------------------



    A)
    4\text{log}_{25}{15} - 4\text{log}_{25}{3}

    4(\text{log}_{25}{15} - \text{log}_{25}{3})

    4\text{log}_{25}{\frac{15}{3}} ...(From property 2)

    4\text{log}_{25}{5}

    4\frac{1}{2} = \boxed{2}

    ---------------------------


    B)
    \frac{1}{3}(\text{log}_{5}{x} + \text{log}_{5}{y}) - 4 \text{log}_{5}{z}

    \text{log}_{(5^3)}{x} + \text{log}_{(5^3)}{y} - 4 \text{log}_{5}{z}

    \text{log}_{(125)}{x} + \text{log}_{(125)}{y} - 4 \text{log}_{125}{z^3}

    \text{log}_{(125)}{xy} - 4 \text{log}_{125}{z^3}

    \text{log}_{(125)}{xy} - \text{log}_{125}{z^{12}}

    \text{log}_{(125)}{\frac{xy}{z^{12}}}

    ---------------------------


    C)
    \text{log}_{2}{20} - \text{log}_{2}{5}

    \text{log}_{2}{4}

    \boxed{2}
    Last edited by wingless; January 15th 2008 at 12:39 PM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Dec 2007
    Posts
    76
    how do you get the 4\frac{1}{2} =4 answer?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member wingless's Avatar
    Joined
    Dec 2007
    From
    Istanbul
    Posts
    585
    Quote Originally Posted by johett View Post
    how do you get the 4\frac{1}{2} =4 answer?
    Typo
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 9
    Last Post: February 22nd 2011, 05:39 PM
  2. Logs
    Posted in the Algebra Forum
    Replies: 4
    Last Post: April 24th 2010, 07:52 AM
  3. Logs
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: October 10th 2009, 06:08 PM
  4. Dealing with Logs and Natural Logs
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: April 14th 2008, 06:18 AM
  5. several questions-logs/natural logs
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: November 12th 2007, 08:58 PM

Search Tags


/mathhelpforum @mathhelpforum