What is the answer to 2^x+8*2^{-x}=9 ?

The answer to 2^x+8*2^{-x}=9 is x=3,x=0

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2^x+8*2^{-x}=9

2^{x} + 8 \cdot 2^{- x} = 9

x = 3, x = 0

Solution steps

2^{x} + 8 \cdot 2^{- x} = 9

Apply exponent rules

2^{x} + 8 (2^{x})^{- 1} = 9

Rewrite the equation with

2^{x} = u

u + 8 (u)^{- 1} = 9

Solve

u + 8 u^{- 1} = 9 : u = 8, u = 1

u = 8, u = 1

Substitute back

u = 2^{x},

solve for

x

Solve

2^{x} = 8 : x = 3

Solve

2^{x} = 1 : x = 0

x = 3, x = 0

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