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

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Homework Help Overview

The problem involves solving the equation log(x) = 2cos(x) within the interval 0 < x < 2π. Participants are exploring the nature of this transcendental equation and its potential solutions.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the possibility of finding solutions through graphical methods and numerical approaches, questioning the feasibility of analytical solutions. There is a suggestion to graph the functions to identify intersection points.

Discussion Status

The discussion is ongoing, with participants exploring different methods to approach the problem. Some have suggested using a calculator to test multiple choice answers, while others are seeking guidance on numerical methods.

Contextual Notes

The problem is presented in a multiple-choice format, which may influence the approach to finding solutions. There is an emphasis on the limitations of analytical methods for this type of equation.

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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