Results 1 to 5 of 5

Math Help - Expanding logarithms

  1. #1
    Newbie
    Joined
    Sep 2008
    Posts
    18

    Expanding logarithms

    I understand the laws of logarithms, they are very simple and I also know how to expand logs but this one has got me stumped because there are 3 square roots. So here is my question.

    Use the Laws of Logarithms to expand the expression.



    I know I can raise the equation to the 1/2 power to get rid of the first square root but then I'm stuck.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    12,114
    Thanks
    992
    \ln\left(\sqrt{x^4\sqrt{y\sqrt{z^2}}}\right) =

    \frac{1}{2}\ln\left(x^4\sqrt{y\sqrt{z^2}}\right) =

    \frac{1}{2}\ln(x^4) + \frac{1}{2} \ln\left(\sqrt{y\sqrt{z^2}}\right) =

    \frac{1}{2}\ln(x^4) + \frac{1}{4} \ln\left(y\sqrt{z^2}\right) =

    \frac{1}{2}\ln(x^4) + \frac{1}{4} \ln(y) + \frac{1}{4}\ln\left(\sqrt{z^2}\right)

    finish up?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Sep 2008
    Posts
    18
    Yeah I should be able to finish it up. I'm just wondering on the 3'rd step why you put 1/2 in front of 2'nd part of the equation. Then for the 4th step you just multiplied the 1/2 by the 1/2 that the second part of the equation would've been raised to?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    12,114
    Thanks
    992
    step 3, justified ...

    \frac{1}{2}\ln\left(x^4\sqrt{y\sqrt{z}}\right) =

    \frac{1}{2}\left[\ln\left(x^4\sqrt{y\sqrt{z^2}}\right)\right] =

    \frac{1}{2}\left[\ln(x^4) + \ln\left(\sqrt{y\sqrt{z^2}}\right)\right] =<br />

    \frac{1}{2}\ln(x^4) + \frac{1}{2}\ln\left(\sqrt{y\sqrt{z^2}}\right)

    for the 4th step, the outer radical only affects the second log term, not the first.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Sep 2008
    Posts
    18
    All right I get it, thanks. I appreciate explaining it to me. The answer is:


    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. expanding logarithms?
    Posted in the Algebra Forum
    Replies: 4
    Last Post: October 15th 2009, 12:46 PM
  2. Expanding
    Posted in the Algebra Forum
    Replies: 7
    Last Post: August 21st 2009, 03:15 PM
  3. expanding logarithms
    Posted in the Pre-Calculus Forum
    Replies: 10
    Last Post: March 11th 2009, 08:27 PM
  4. Help expanding log?
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: February 13th 2009, 06:31 PM
  5. expanding expression using properties of logarithms
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: November 21st 2008, 03:17 PM

Search Tags


/mathhelpforum @mathhelpforum