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!

Logarithm defined as integral

  1. Apr 25, 2006 #1
    Confused, but tried it this way:

    Use u-substitution to show that (for y a positive number and x>0)

    [tex]\int_{x}^{xy} \frac{1}{t} dt = \int_{1}^{y} \frac{1}{t} dt [/tex]

    so, u=t and du=dt
    if x=1
    t=xy u=y(1)=y
    t=x u=1

    u=1/t and du/ln [t] = dt
    if x=1
    t=xy u=1/y
    t=x y=1

    Thanks for your help
  2. jcsd
  3. Apr 25, 2006 #2


    User Avatar
    Science Advisor

    That's not a very useful substitution, is it?
    but x is not 1.

    No, if u= 1/t, then du= -dt/t2
    Again, you cannot just say "if x= 1"- it's not, it's a variable. Also you haven't used those substitutions- you haven't put them into either integral.

    Look at the upper limits on each integral. On one it is xy, on the other it is just y. To show that the two integrals are equal, you need to change one into the other by some substitution. Okay,xy/x= y so we need to divide by x. Try u= t/x in the left integral only.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Threads - Logarithm defined integral Date
Convergence of a series with n-th term defined piecewise Feb 26, 2018
Logarithmic integration Jan 27, 2018
Discrete logarithm property Jan 16, 2018
Find the derivative of this function Jan 12, 2018
Using logarithms in vector Calculus Jan 8, 2018