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

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

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

2^{x - 1} + 2^{- x} = 1 \frac{1}{2}

x = 1, x = 0

Solution steps

2^{x - 1} + 2^{- x} = 1 \frac{1}{2}

Convert mixed numbers to improper fractions:

1 \frac{1}{2} = \frac{3}{2}

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

Apply exponent rules

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

Rewrite the equation with

2^{x} = u

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

Solve

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

19.972 = a^{120 - h} + k

e^{- 0.1 x + 1} = 1

(7^{3 x})^{3} = 243

2^{x - 1} = \frac{1}{8}

2 5^{x + 2} = 5^{x^{2} + 6 x + 7}

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