How Do You Solve the Equation log(x) = 2cos(x) in the Interval 0 < x < 2π?

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To solve the equation log(x) = 2cos(x) in the interval 0 < x < 2π, graphical methods are suggested to identify the intersection points of the two functions. The problem is classified as a transcendental equation, indicating it cannot be solved analytically. Participants discuss using numerical methods to find solutions, particularly since it is presented as a multiple-choice question. Suggestions include plugging in the answer choices into a calculator to verify which values satisfy the equation. Ultimately, the discussion emphasizes the need for numerical approaches or graphical analysis to find the correct solutions.
ms. confused
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How does this question work? It's multiple choice so its one of the following answers.

logx=2cosx, 0<x<2pi

A. 0.17, 0.71
B. 1.38
C. 1.48, 5.07
D. 1.57, 5.11
 
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Graphical Solution

There is an x (in your domain) where these two functions intersect. Graph them and see. (This is a trancendental equation, by the way.)

-Beth
 
If it's multiple choice, why don't you plug in the values in your calc?

If you want a method, I don't think this can be solved analytically. Do you know any numerical methods?
 
daster said:
Do you know any numerical methods?

That's what I was hoping to find out.
 

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