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

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

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

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

a = 3, a = 2

Solution steps

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

Apply exponent rules

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

Rewrite the equation with

2^{a} = 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^{a},

solve for

a

Solve

2^{a} = 8 : a = 3

Solve

2^{a} = 4 : a = 2

a = 3, a = 2

2^{x} + 2^{3} x = 16

2^{x} = 0.5

m, 2^{n} \cdot n = 2^{m}

5^{2 x - 1} - 10 (x^{5})^{x - 1} - 75 = 0

2^{3 + x} = 5^{x - 4}

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