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

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

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

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

x = 1, x = 0

Solution steps

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

Apply exponent rules

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

Rewrite the equation with

2^{x} = u

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

Solve

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

u = 2, u = 1

Substitute back

u = 2^{x},

solve for

x

Solve

2^{x} = 2 : x = 1

Solve

2^{x} = 1 : x = 0

x = 1, x = 0

2^{x} = \frac{1}{16}

10 0^{x - 1} = 100 0^{2 x}

4^{x} = 1

4^{x} = 3

5^{(x + 1)} = 25