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

The answer to 2^{2x+1}+2^x=3 is x=0

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

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

x = 0

Solution steps

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

Apply exponent rules

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

Rewrite the equation with

2^{x} = u

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

Solve

u^{2} \cdot 2^{1} + u = 3 : u = 1, u = - \frac{3}{2}

u = 1, u = - \frac{3}{2}

Substitute back

u = 2^{x},

solve for

x

Solve

2^{x} = 1 : x = 0

Solve

2^{x} = - \frac{3}{2} :

No Solution for

x \in R

x = 0

x, e^{x y} y = 0

x, 5^{x} = 3

1200 = 500 e^{x}

2 e^{- x} = e^{3 x - 4}

6^{3 x^{2}} = \frac{1}{3 6 ^{3 x + 1}}