Results 1 to 2 of 2

Thread: Logs

  1. #1
    Newbie
    Joined
    Nov 2009
    Posts
    23

    Logs

    Given that logab(a)=4, calculate logab 3√a /√b. Start with the exponent property of logs, then the quotient rule, and then change of base.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Grandad's Avatar
    Joined
    Dec 2008
    From
    South Coast of England
    Posts
    2,570
    Thanks
    1
    Hello KingV15
    Quote Originally Posted by KingV15 View Post
    Given that logab(a)=4, calculate logab 3√a /√b. Start with the exponent property of logs, then the quotient rule, and then change of base.
    I'm guessing that the question is:
    Given $\displaystyle \log_{ab}(a) = 4$, calculate $\displaystyle \log_{ab}\left(\frac{\sqrt[3]{a}}{\sqrt{b}}\right)$
    (The alternative is that you have to calculate $\displaystyle \log_{ab}\left(\frac{3\sqrt{a}}{\sqrt{b}}\right)$, which will leave a term in $\displaystyle \log_{ab}(3)$ at the end.)

    So, if my assumption is correct:
    $\displaystyle \log_{ab}(a) = 4$

    $\displaystyle \Rightarrow (ab)^4 = a$

    $\displaystyle \Rightarrow a^4b^4 = a$

    $\displaystyle \Rightarrow b^4 = a^{-3}$

    $\displaystyle \Rightarrow b = a ^{-\frac34}$
    And then:
    $\displaystyle \log_{ab}\left(\frac{\sqrt[3]{a}}{\sqrt{b}}\right)=\tfrac13\log_{ab}(a) - \tfrac12\log_{ab}(b)$
    $\displaystyle =\tfrac13\log_{ab}(a) - \tfrac12\log_{ab}(a^{-\frac34})$

    $\displaystyle =\tfrac13\log_{ab}(a) - \tfrac12\times(-\tfrac34)\log_{ab}(a)$

    $\displaystyle =(\tfrac13+\tfrac38)\log_{ab}(a)$

    $\displaystyle =\frac{17}{24}\times 4$

    $\displaystyle =\frac{17}{6}$
    (The answer to the alternative question is, using a similar method, $\displaystyle \frac72+\log_{ab}(3)$.)
    Grandad
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

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

Search tags for this page

Click on a term to search for related topics.

Search Tags


/mathhelpforum @mathhelpforum