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

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

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

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

x = 3, x = 2

Solution steps

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

Apply exponent rules

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

Rewrite the equation with

2^{x} = u

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

Solve

u \cdot 2^{- 2} + u^{- 1} \cdot 2^{3} = 3 : u = 8, u = 4

u = 8, u = 4

Substitute back

u = 2^{x},

solve for

x

Solve

2^{x} = 8 : x = 3

Solve

2^{x} = 4 : x = 2

x = 3, x = 2

(3^{8}) 4 = 3^{x}

2 = 1.0 5^{x}

1 6^{x} - 2^{2 x + 4} - 4^{x} + 16 = 0

7^{x - 3} = 1

4 x - 5. 2^{x} + 4 = 0

What is the answer to 2^{x-2}+2^{3-x}=3 ?
The answer to 2^{x-2}+2^{3-x}=3 is x=3,x=2
Solve for x: 2^{x-2}+2^{3-x}=3
The solution is x=3,x=2