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: Trippy Log Functions

  1. Apr 30, 2006 #1
    I graphed y=logx+log2x and y=log2x^2 and the graphs came out a lot different. However when you simplify y=logx+log2x you actually get y=log2x^2!! Any ideas about why the graphs are so different yet the equations are pretty much the same? thanx
  2. jcsd
  3. Apr 30, 2006 #2


    User Avatar
    Gold Member

    Well notice that log(a) outputs real numbers only if a>0.

    With that in mind, when x<0, in your first equation the inputs to the logs are negative so that function is not defined if you are graphing real numbers. The second equation is defined for x<0 because x2 yields a positive value.

    If you look at the two graphs they are identical when x>0. When x<0, the first graph is undefined while the second graph is just an even extension of when x>0.

    Just as a note, when you are dealing with the function y=log(x)+log(2x), the domain that yields a real result is x>0. If you simplify the expression to y=log(2x2) then you have to remember that your domain is still x>0. In that sense the two functions are identical.
    Last edited: Apr 30, 2006
  4. Apr 30, 2006 #3


    User Avatar
    Science Advisor

    In other words, log a+ log b= log ab if and only if log a and log b both exist- that is, as long as a and b are both positive. If a and b are both negative, log ab exists even though log a and log b do not.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook