What is the answer to 2^{2x-7}-9*2^{x-1}+256=0 ?

The answer to 2^{2x-7}-9*2^{x-1}+256=0 is x=9,x=6

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2^{2x-7}-9*2^{x-1}+256=0

2^{2 x - 7} - 9 \cdot 2^{x - 1} + 256 = 0

x = 9, x = 6

Solution steps

2^{2 x - 7} - 9 \cdot 2^{x - 1} + 256 = 0

Apply exponent rules

(2^{x})^{2} \cdot 2^{- 7} - 9 \cdot 2^{x} \cdot 2^{- 1} + 256 = 0

Rewrite the equation with

2^{x} = u

(u)^{2} \cdot 2^{- 7} - 9 u \cdot 2^{- 1} + 256 = 0

Solve

u^{2} \cdot 2^{- 7} - 9 u \cdot 2^{- 1} + 256 = 0 : u = 512, u = 64

u = 512, u = 64

Substitute back

u = 2^{x},

solve for

x

Solve

2^{x} = 512 : x = 9

Solve

2^{x} = 64 : x = 6

x = 9, x = 6

x, 3 e^{x} = 5 + 8 e^{- x}

4^{2 x + 1} = 0. 5^{3 x + 2}

9^{x + 1} = 2 7^{2 x - 5}

x, e^{x y} = 2

What is the answer to 2^{2x-7}-9*2^{x-1}+256=0 ?
The answer to 2^{2x-7}-9*2^{x-1}+256=0 is x=9,x=6
Solve for x: 2^{2x-7}-9*2^{x-1}+256=0
The solution is x=9,x=6