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

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

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

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

x = 1

Solution steps

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

Apply exponent rules

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

Rewrite the equation with

e^{x} = u

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

Solve

u^{2} - 2 u e^{1} + e^{2} = 0 : u = e

u = e

Substitute back

u = e^{x},

solve for

x

Solve

e^{x} = e : x = 1

x = 1

4^{- x} = \frac{1}{64}

2^{2 x + 3} + 2^{x + 3} = 2^{0} + 2^{x}

2^{x + 3} = 8

e^{x} + x - 3 = 0

e^{x} = 13.8

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