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Solve the equation (2^2x)/( 2^x+5) = 1 algebraically using two different initial steps as directed below.
. Write each side as a power of 2

Respuesta :

Answer:

x = 5

Step-by-step explanation:

Given equation as:

[tex]\frac{2^2x}{2^{x+5}}[/tex] = 1

now,

writing each side as power of 2

2⁰ = 1

therefore,

[tex]\frac{2^2x}{2^{x+5}}[/tex] = 2⁰

also, we know the property that , when the number having the same bases gets divided , the powers of the number gets subtracted

therefore,

[tex]2^{2x-(x+5)}[/tex]  = 2⁰

now for the equality the power of 2 both sides should be equal

thus,

⇒ 2x-(x+5) = 0

or

⇒ 2x = x + 5

or

⇒ 2x - x = 5

or

⇒ x = 5

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