What is the answer to 2^{2x-2}-2^{x+1}=2^x-2^3 ?

The answer to 2^{2x-2}-2^{x+1}=2^x-2^3 is x=3,x=2

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2^{2x-2}-2^{x+1}=2^x-2^3

2^{2 x - 2} - 2^{x + 1} = 2^{x} - 2^{3}

x = 3, x = 2

Solution steps

2^{2 x - 2} - 2^{x + 1} = 2^{x} - 2^{3}

Apply exponent rules

(2^{x})^{2} \cdot 2^{- 2} - 2^{x} \cdot 2^{1} = 2^{x} - 2^{3}

Rewrite the equation with

2^{x} = u

(u)^{2} \cdot 2^{- 2} - u \cdot 2^{1} = u - 2^{3}

Solve

u^{2} \cdot 2^{- 2} - u \cdot 2^{1} = u - 2^{3} : 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^{3 - 2 x} = 4

2 (3^{2 x - 1}) = 4^{x + 1}

4^{3 x} = 32

3^{x + 1} + 3^{x} + 3^{x - 1} = 117

3 (2^{2 x}) = 0.75

What is the answer to 2^{2x-2}-2^{x+1}=2^x-2^3 ?
The answer to 2^{2x-2}-2^{x+1}=2^x-2^3 is x=3,x=2
Solve for x: 2^{2x-2}-2^{x+1}=2^x-2^3
The solution is x=3,x=2