What is the answer to 4^{-x}-2^{-x+2}+4=0 ?

The answer to 4^{-x}-2^{-x+2}+4=0 is x=-1

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4^{-x}-2^{-x+2}+4=0

4^{- x} - 2^{- x + 2} + 4 = 0

x = - 1

Solution steps

4^{- x} - 2^{- x + 2} + 4 = 0

Apply exponent rules

(2^{x})^{- 2} - (2^{x})^{- 1} \cdot 2^{2} + 4 = 0

Rewrite the equation with

2^{x} = u

(u)^{- 2} - (u)^{- 1} \cdot 2^{2} + 4 = 0

Solve

u^{- 2} - u^{- 1} \cdot 2^{2} + 4 = 0 : u = \frac{1}{2}

u = \frac{1}{2}

Substitute back

u = 2^{x},

solve for

x

Solve

2^{x} = \frac{1}{2} : x = - 1

x = - 1

x^{x} = \frac{1}{2}

7 e^{2 x + 3} = 20

4^{x} - 3 \cdot 2^{x + 2} + 32 = 0

27 = 3^{x + 1}

9^{1 - 7 x} = 24 3^{x - 11}

What is the answer to 4^{-x}-2^{-x+2}+4=0 ?
The answer to 4^{-x}-2^{-x+2}+4=0 is x=-1
Solve for x: 4^{-x}-2^{-x+2}+4=0
The solution is x=-1