What is the answer to 4^{x+1}-2^{x+2}+1=0 ?

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

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4^{x+1}-2^{x+2}+1=0

4^{x + 1} - 2^{x + 2} + 1 = 0

x = - 1

Solution steps

4^{x + 1} - 2^{x + 2} + 1 = 0

Apply exponent rules

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

Rewrite the equation with

2^{x} = u

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

Solve

u^{2} \cdot 2^{2} - u \cdot 2^{2} + 1 = 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

5^{x + 1} = 100 (3)^{x}

11 e^{- 4 x} = 21

2 \cdot 3^{x} + 5 = 17

300 \cdot 1 0^{x} = 20 \cdot 2 0^{x}

\frac{1}{4} = e^{- x}

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