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

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

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

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

x = 0

Solution steps

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

Apply exponent rules

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

Rewrite the equation with

2^{x} = u

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

Solve

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

u = 1

Substitute back

u = 2^{x},

solve for

x

Solve

2^{x} = 1 : x = 0

x = 0

e^{2 x + 3} = 3

2^{3 x + 1} - 2^{3 x - 1} = 96

2^{x} = 16000

105 0^{x} + 105 0^{x + 1} + 105 0^{x + 2} = 2021

4^{x} = 26

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