What is the answer to 4^{x+1}-5(2^x)+1=0 ?

The answer to 4^{x+1}-5(2^x)+1=0 is x=0,x=-2

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4^{x+1}-5(2^x)+1=0

4^{x + 1} - 5 (2^{x}) + 1 = 0

x = 0, x = - 2

Solution steps

4^{x + 1} - 5 (2^{x}) + 1 = 0

Apply exponent rules

(2^{x})^{2} \cdot 2^{2} - 5 \cdot 2^{x} + 1 = 0

Rewrite the equation with

2^{x} = u

(u)^{2} \cdot 2^{2} - 5 u + 1 = 0

Solve

u^{2} \cdot 2^{2} - 5 u + 1 = 0 : u = 1, u = \frac{1}{4}

u = 1, u = \frac{1}{4}

Substitute back

u = 2^{x},

solve for

x

Solve

2^{x} = 1 : x = 0

Solve

2^{x} = \frac{1}{4} : x = - 2

x = 0, x = - 2

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

9^{8 - x} = 2 7^{x - 3}

- 12 e^{- x} + 8 = 7

5^{x} + 5^{- x} = 2

1 - e^{\frac{- x}{50}} = 0.25

What is the answer to 4^{x+1}-5(2^x)+1=0 ?
The answer to 4^{x+1}-5(2^x)+1=0 is x=0,x=-2
Solve for x: 4^{x+1}-5(2^x)+1=0
The solution is x=0,x=-2