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February 25th, 2017, 09:00 PM   #1
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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
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February 25th, 2017, 09:02 PM   #2
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Math Focus: Yet to find out.
Do you want an answer or a solution..

Wolfram|Alpha: Computational Knowledge Engine
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February 25th, 2017, 09:03 PM   #3
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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?
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February 25th, 2017, 09:32 PM   #4
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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.
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February 25th, 2017, 09:34 PM   #5
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Quote:
Originally Posted by sothirtyyearsago View Post
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 $x \approx 1.69$
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February 25th, 2017, 09:59 PM   #6
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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.
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February 25th, 2017, 10:06 PM   #7
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Quote:
Originally Posted by sothirtyyearsago View Post
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.
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