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

In summary, To solve the equation e^x + e^-x = 4, you can substitute u=e^x and rewrite the equation as a quadratic equation in u. This can then be solved using the quadratic formula. The solutions are +/- 1.3169. Multiplying both sides of the equation by u will give the solution.
  • #1
Chiborino
21
0
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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  • #2
If you put u=e^x then e^(-x)=1/u. So it becomes quadratic equation in u. Is that enough of a hint?
 
  • #3
I'm not entirely sure I see how u+1/u can be plugged into the quadratic formula.

Could you please elaborate?
 
  • #4
u+1/u=4. Multiply both sides by u.
 
  • #5
Oh... I feel kind of dumb now. >_>
Thanks much.
 

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

What are exponential variables?

Exponential variables are mathematical variables that are raised to a power. They can be written in the form of ax, where a is a constant and x is the variable.

What is e in exponential variables?

e is a mathematical constant, also known as Euler's number, that is approximately equal to 2.71828. It is commonly used in exponential functions and is an important constant in calculus.

What is the equation ex + e-x = 4?

This equation is an exponential equation that involves the variable x and the constant e. It is a type of exponential function known as a hyperbolic function, and is often used in physics and engineering.

How can I solve ex + e-x = 4?

To solve this equation, you can use logarithms or graphing techniques. One method is to rewrite the equation as e2x - 4ex + 1 = 0 and then use the quadratic formula to find the values of x. Another method is to graph both sides of the equation and find the intersection point.

Why is mastering exponential variables important?

Exponential variables are used in many fields of science and mathematics, such as biology, economics, and physics. By mastering how to solve equations involving exponential variables, you can better understand and analyze complex systems and make accurate predictions.

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