Mastering Exponential Variables: How to Solve e^x + e^-x = 4 with Ease

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Homework Help Overview

The problem involves solving the equation e^x + e^-x = 4, which falls under the topic of exponential functions and their properties. Participants are exploring methods to manipulate the equation to find the value of x.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • The original poster expresses confusion about how to start solving the equation despite previous attempts using factoring and logarithms. Some participants suggest substituting u = e^x to transform the equation into a quadratic form, while others seek clarification on how to apply the quadratic formula to the new expression.

Discussion Status

The discussion is ongoing, with participants providing hints and exploring different approaches. There is an acknowledgment of the transformation into a quadratic equation, but clarity on the application of the quadratic formula is still being sought.

Contextual Notes

The original poster mentions feeling unprepared for the problem despite having a background in precalculus, indicating a potential gap in understanding exponential equations. There is also a reference to a graphing calculator providing numerical solutions, which may influence the discussion.

Chiborino
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My friend just came to me with this problem:
e^x + e^-x = 4
I aced precalc, and I still have no idea where to start on this one. I've factored, natural logged, factored and then natural logged... and I keep running into dead ends.

My graphing calculator puts the answer at +/-1.3169 or something like that.

It's not at all urgent, I'm just curious since I feel that I should know how to solve this problem.
 
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If you put u=e^x then e^(-x)=1/u. So it becomes quadratic equation in u. Is that enough of a hint?
 
I'm not entirely sure I see how u+1/u can be plugged into the quadratic formula.

Could you please elaborate?
 
u+1/u=4. Multiply both sides by u.
 
Oh... I feel kind of dumb now. >_>
Thanks much.
 

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