What is the answer to 2^{2x-2}-3*2^x+8=0 ?

The answer to 2^{2x-2}-3*2^x+8=0 is x=3,x=2

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2^{2x-2}-3*2^x+8=0

2^{2 x - 2} - 3 \cdot 2^{x} + 8 = 0

x = 3, x = 2

Solution steps

2^{2 x - 2} - 3 \cdot 2^{x} + 8 = 0

Apply exponent rules

(2^{x})^{2} \cdot 2^{- 2} - 3 \cdot 2^{x} + 8 = 0

Rewrite the equation with

2^{x} = u

(u)^{2} \cdot 2^{- 2} - 3 u + 8 = 0

Solve

u^{2} \cdot 2^{- 2} - 3 u + 8 = 0 : u = 8, u = 4

u = 8, u = 4

Substitute back

u = 2^{x},

solve for

x

Solve

2^{x} = 8 : x = 3

Solve

2^{x} = 4 : x = 2

x = 3, x = 2

e^{(x^{2} - 2 x)} = 1

6^{2 x - 2} = 4^{3 x - 9}

e^{3 x} = e^{6 x}

(n x)^{x} = n^{n^{n}}

e^{2 x} = (e^{x})^{2}

What is the answer to 2^{2x-2}-3*2^x+8=0 ?
The answer to 2^{2x-2}-3*2^x+8=0 is x=3,x=2
Solve for x: 2^{2x-2}-3*2^x+8=0
The solution is x=3,x=2