What is the answer to 4^x-9*2^{x-1}+2=0 ?

The answer to 4^x-9*2^{x-1}+2=0 is x=2,x=-1

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4^x-9*2^{x-1}+2=0

4^{x} - 9 \cdot 2^{x - 1} + 2 = 0

x = 2, x = - 1

Solution steps

4^{x} - 9 \cdot 2^{x - 1} + 2 = 0

Apply exponent rules

(2^{x})^{2} - 9 \cdot 2^{x} \cdot 2^{- 1} + 2 = 0

Rewrite the equation with

2^{x} = u

(u)^{2} - 9 u \cdot 2^{- 1} + 2 = 0

Solve

u^{2} - 9 u \cdot 2^{- 1} + 2 = 0 : u = 4, u = \frac{1}{2}

u = 4, u = \frac{1}{2}

Substitute back

u = 2^{x},

solve for

x

Solve

2^{x} = 4 : x = 2

Solve

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

x = 2, x = - 1

2 e^{2 x} - e^{x} = 0

0 = e^{- x}

e^{y} = 9

e^{2 x} - 6 e^{x} + 8 = 0

x^{2} e^{2 x} + 2 x e^{2 x} = 8 e^{2 x}

What is the answer to 4^x-9*2^{x-1}+2=0 ?
The answer to 4^x-9*2^{x-1}+2=0 is x=2,x=-1
Solve for x: 4^x-9*2^{x-1}+2=0
The solution is x=2,x=-1