My Math Forum x intercept with cosine and natural log equations

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 February 25th, 2017, 09:00 PM #1 Newbie   Joined: Feb 2017 From: Canada Posts: 3 Thanks: 0 x intercept with cosine and natural log equations I've got a math question I'm trying to figure out, but it's been so long since I studied math that it's all a blur now. Any help or guidance would be great. You can probably tell by my username how long ago all this was... Find the x intercept where y = e^cos x and y = x * ln x
 February 25th, 2017, 09:02 PM #2 Senior Member   Joined: Feb 2016 From: Australia Posts: 1,764 Thanks: 623 Math Focus: Yet to find out. Do you want an answer or a solution.. Wolfram|Alpha: Computational Knowledge Engine Thanks from sothirtyyearsago
 February 25th, 2017, 09:03 PM #3 Senior Member   Joined: Aug 2012 Posts: 2,156 Thanks: 630 The x-intercept is the point where y = 0. Since the exponential function is never zero, e^cos x has no x-intercept. Did you mean the point of intersection of the two graphs? Thanks from sothirtyyearsago
 February 25th, 2017, 09:32 PM #4 Newbie   Joined: Feb 2017 From: Canada Posts: 3 Thanks: 0 Sorry, I meant find the x coordinate of the point of intersection of the two y equations. I tried that Wolframalpha, but it said the computation time was exceeded so going Pro would be needed. Maybe some direction and pointers would be good. I was Googling e and log functions and how to factor them down which looked familiar, but that cosine of x is throwing things off I think.
February 25th, 2017, 09:34 PM   #5
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Quote:
 Originally Posted by sothirtyyearsago Sorry, I meant find the x coordinate of the point of intersection of the two y equations. I tried that Wolframalpha, but it said the computation time was exceeded so going Pro would be needed. Maybe some direction and pointers would be good. I was Googling e and log functions and how to factor them down which looked familiar, but that cosine of x is throwing things off I think.
Joppy's link comes right up for me.

The solution is $x \approx 1.69$

 February 25th, 2017, 09:59 PM #6 Newbie   Joined: Feb 2017 From: Canada Posts: 3 Thanks: 0 Oops I didn't click the link. I was at that Wolfram site previously and entered the two equations, but I see the link provided does work. I must have entered them incorrectly. I didn't put brackets around cos x. Could you show me the work involved in getting to the x calculation? Last edited by sothirtyyearsago; February 25th, 2017 at 10:02 PM.
February 25th, 2017, 10:06 PM   #7
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Quote:
 Originally Posted by sothirtyyearsago Oops I didn't click the link. I was at that Wolfram site previously and entered the two equations, but I see the link provided does work. I must have entered them incorrectly. I didn't put brackets around cos x. Could you show me the work involved in getting to the x calculation?
it has to be solved using numeric methods. There isn't going to be a closed form solution for $x$

Here is one example of a commonly used numeric method.

 Tags cosine, equations, intercept, log, natural

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