Results 1 to 8 of 8

Math Help - express in terms log(x) log(y)

  1. #1
    Member
    Joined
    Feb 2009
    Posts
    101
    Awards
    1

    express in terms log(x) log(y)

    the question is...

    \frac{1}{2}log(\frac{\sqrt{x}}{xy})

    my attempt...

    \frac{1}{2}log\sqrt{x}-\frac{1}{2}log(xy)

    log{x}-\frac{1}{2}log(xy)

    the bit what i was unsire about was the sqrt

    many thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member Quacky's Avatar
    Joined
    Nov 2009
    From
    Windsor, South-East England
    Posts
    901


    Note that \sqrt x = x^{\frac{1}{2}}

    Also note that log(xy) = log(x)+log(y)

    So to start, I would say:



    =\frac{1}{2}log(x^\frac{1}{2})-\frac{1}{2}Log(xy)

    How would you continue to simplify?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Feb 2009
    Posts
    101
    Awards
    1
    im geting a bit confused with the simplifying.

    do i remove the 1/2 by multipying by 2?

    and im unsure how i would bring the x of the xy to the other side?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member Quacky's Avatar
    Joined
    Nov 2009
    From
    Windsor, South-East England
    Posts
    901


    Let's split this up and simplify the

    \frac{1}{2}log(x^\frac{1}{2}) first.

    Do you recall that

    Log(a^b)=b\times log(a)?

    How would you apply that rule here?

    Now let's look at:

    -\frac{1}{2}log(xy)

    = -\frac{1}{2} [log(xy)]

    Now, to simplify this, why not just apply the

    rule?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Feb 2009
    Posts
    101
    Awards
    1
    \frac{1}{2}(-\frac{1}{2}log(x)+log(y)) ?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Super Member Quacky's Avatar
    Joined
    Nov 2009
    From
    Windsor, South-East England
    Posts
    901
    Edit, nevermind, will edit in a sec.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Super Member Quacky's Avatar
    Joined
    Nov 2009
    From
    Windsor, South-East England
    Posts
    901


     <br />
=\frac{1}{2}\times\frac{1}{2}Log(x)-\frac{1}{2}[Log(x)+Log(y)]<br />

    =\frac{1}{4}Log(x)-\frac{1}{2}log(x)-\frac{1}{2}Log(y)

    =\frac{1}{2}[\frac{1}{2}Log(x)-Log(x)-Log(y)]

    =\frac{1}{2}[-\frac{1}{2}Log(x)-Log(y)]

    I think that this is correct, I'll check in a second. So you just made a sign error somewhere.

    Edit: I've checked, and it seems that I am correct. I must apologize for the late reply - I was caught on my PC when I should have been asleep, so I was forced to turn it off abrutly.
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Member
    Joined
    Feb 2009
    Posts
    101
    Awards
    1
    thank you for your help
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Given that y = (x-a)/(x+b), express in terms of a, b and y
    Posted in the Algebra Forum
    Replies: 4
    Last Post: September 19th 2011, 05:43 AM
  2. express in terms of x
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: August 24th 2009, 08:34 PM
  3. Express log in Terms of x and y
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: April 20th 2009, 06:58 AM
  4. express y in terms of x
    Posted in the Algebra Forum
    Replies: 3
    Last Post: January 29th 2009, 10:02 PM
  5. express sin x/2 in terms of cos x
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: November 15th 2007, 08:23 PM

Search Tags


/mathhelpforum @mathhelpforum