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!

B Strange logarithmic property

  1. Jan 26, 2017 #1
    I encountered this in http://calcchat.com/book/Calculus-10e/8/4/7/

    Capture.PNG


    How come the above expression equals the below?
    What I know it should be 4 ln(x/(4+sqrt(16-x^2))) which means the -1 becomes the power of that thing inside ln.

    Please help me. I really don't get it.
     
  2. jcsd
  3. Jan 26, 2017 #2

    andrewkirk

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Provided ##x\in[-4,0)\cup (0,4]## we have
    $$\left|\frac{4+\sqrt{16-x^2}}x\right|=\frac{4+\sqrt{16-x^2}}{|x|}$$
    and
    $$\left|\frac{4-\sqrt{16-x^2}}x\right|=\frac{4-\sqrt{16-x^2}}{|x|}$$
    and that multiplying the two right-hand sides together gives 1. So they are reciprocals, hence their logs are additive inverses.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted