What is the solution to 2^x + 2^-x = 3?

  • Thread starter Andolph23
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In summary, the value of x in the equation 2^x + 2^-x = 3 cannot be determined without additional information. This equation can be solved using logarithms or algebraic methods, but they may not always yield exact solutions. The equation represents an exponential and reciprocal function. There are real solutions to this equation, but the number and values may vary depending on the context.
  • #1
Andolph23
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The Attempt at a Solution



2^x + 2^-x = 3

2^x + (1 / ((2^x)) = 3

(4^((x^2)) +1) / (2^x) = 3

(4^((x^2)) + 1) = 6^ x
 
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  • #2
No, 2(3^x) is not the same 6^x.
 
  • #3
Multiply both sides by 2x instead.
 
  • #4
My bad. I forgot that they must have the same base to multiply them. Also, If you're referring to the last step, I did multiply both sides by 2^x. I'm stuck at that point though.
 
  • #5
let u = 2^x
solve the quadratic
after solve for u solve for x
 
  • #6
Thanks that helped a lot. Thanks everyone for the quick replies
 

FAQ: What is the solution to 2^x + 2^-x = 3?

What is the value of x in the equation 2^x + 2^-x = 3?

The value of x in this equation cannot be determined without additional information. The equation can have multiple solutions depending on the given context or constraints.

How can I solve the equation 2^x + 2^-x = 3?

This equation can be solved using logarithms. By taking the logarithm of both sides, the equation can be simplified to xln2 + (-x)ln2 = ln3. From there, x can be isolated and solved for.

Can this equation be solved using algebraic methods?

Yes, this equation can be solved using algebraic methods such as factoring or the quadratic formula. However, these methods may not always yield exact solutions and may require the use of approximations.

What type of function does this equation represent?

This equation represents an exponential function, as the variable x appears as an exponent in both terms. The presence of a negative exponent also indicates a reciprocal function.

Are there any real solutions to this equation?

Yes, there are real solutions to this equation. However, the number of solutions and their values may vary depending on the context of the problem. In some cases, there may be no real solutions or an infinite number of solutions.

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