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Using a table of values, determine the solution to the equation below to the nearest fourth of a unit.

2^(-x) - 2 = 4^x - 1

x ≈ -1
x ≈ -0.75
x ≈ 0
x ≈ -0.50

Respuesta :

Matheng
[tex] 2^{-x-2} = 4^{x-1} [/tex]
∵ 4 = 2²
[tex] 2^{-x-2} =2^{2(x-1)} [/tex]

The bases are equals
So the powers should be equal
∴ -x-2 = 2(x-1)
solve for x
∴ x = 0


Eduard22sly

The solution to the equation 2⁻ˣ⁻² = 4ˣ⁻¹ to the nearest fourth of a unit is x = 0

Data obtained from the question

  • Equation = 2⁻ˣ⁻² = 4ˣ⁻¹
  • Value of x =?

How to determine the value of x

2⁻ˣ⁻² = 4ˣ⁻¹

Recall

4 = 2²

Thus,

2⁻ˣ⁻² = 2²⁽ˣ⁻¹⁾

-x - 2 = 2(x - 1)

Clear bracket

-x - 2 = 2x - 2

Collect like terms

-x - 2x = -2 + 2

-3x = 0

Divide both sides by -3

x = 0 / -3

x = 0

Thus, the solution to the equation is x = 0

Learn more about algebra:

brainly.com/question/2768008

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