1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Natural log equation

  1. Jul 31, 2008 #1
    1. The problem statement, all variables and given/known data

    sqrt(ln(x)) = ln(sqrt(x))

    2. Relevant equations

    3. The attempt at a solution

    I've been trying to do this for some time now. Could anyone give some tips on how to get started with this?
  2. jcsd
  3. Jul 31, 2008 #2
    Try squaring both sides and then bring the ln over.
  4. Jul 31, 2008 #3
    (ln(sqrt(x))^2 - ln x = 0

    2 * ln(sqrt(x)) - ln x = 0

    ln (sqrt(x)) (2-ln(sqrt(x))) = 0

    x=1 and e^4.

    Ok got it now. I tried this for 10+ minutes and was totally lost. Somehow brain starts to work a little after posting here :P
    Last edited: Jul 31, 2008
  5. Aug 1, 2008 #4
    Haha yeah happens sometimes.

    Btw, what do u mean by:
    2 * ln(sqrt(x)) - ln x = 0

    this is what i did:

    After squaring:
    ln(x) = ln (x^1/2)*ln(x^1/2)
    Bring the half down:
    ln(x) = 1/2(ln(x))*1/2(ln(x))
    then after a bit of rearranging:
    1/4(ln(x)ln(x)) - ln(x) = 0.
    Factor the ln(x) out.
    ln(x)[1/4(lnx) -1] = 0.
    ln x = 0 or 1/4lnx = 1
    x = e^0
    =1 or lnx = 4, x = e^4
  6. Aug 1, 2008 #5
    After the first line above, the rest of your manipulations don't seem valid. [ln(sqrt(x))]^2 does NOT equal 2 * ln(sqrt(x)). 2 * ln(sqrt(x)) = ln[(sqrt(x))^2]. See the difference?

    Similarly ln(sqrt(x)) * ln(sqrt(x)) does NOT equal ln(x). Only the addition of two logs with the same base allows for the arguments to be multiplied together. I think you need to check your rules again.
  7. Aug 1, 2008 #6


    User Avatar
    Science Advisor

    [tex]\sqrt{ln(x)}= ln(\sqrt{x})[/tex]

    I think I would have been inclined to write this as
    [tex]\sqrt{ln(x)}= (1/2)ln(x)[/tex]
    and let u= ln(x) so I have
    [tex]\sqrt{u}= (1/2)u[/tex]
    or u= u2/4. Then, then, is equivalent to u2- 4u= 0 which has u= 0 and u= 4 as solutions. Since u= ln(x), u= 0 gives x= 1 and u= 4 gives u= e4.
  8. Aug 1, 2008 #7
    Yea i made a mistake there. I was fixing it yesterday but it said can't edit after 1 hour. This is how I did it.

    square both sides and factor ln(sqrt(x)) out.

    ln x = (ln sqrt(x))^2

    ln(sqrt(x)) (ln(sqrt(x)) - 2) = 0

    ln(sqrt(x)) = 0 and ln(sqrt(x)) - 2 = 0

    x=1 x=e^4

    It's good to see different ways of doing it :)
    Thanks for the help, please tell me if there's any mistake in this.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook