What is the answer to 2^{2x+8}-8*2^{x+2}+1=0 ?

The answer to 2^{2x+8}-8*2^{x+2}+1=0 is x=-4

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2^{2x+8}-8*2^{x+2}+1=0

2^{2 x + 8} - 8 \cdot 2^{x + 2} + 1 = 0

x = - 4

Solution steps

2^{2 x + 8} - 8 \cdot 2^{x + 2} + 1 = 0

Apply exponent rules

(2^{x})^{2} \cdot 2^{8} - 8 \cdot 2^{x} \cdot 2^{2} + 1 = 0

Rewrite the equation with

2^{x} = u

(u)^{2} \cdot 2^{8} - 8 u \cdot 2^{2} + 1 = 0

Solve

u^{2} \cdot 2^{8} - 8 u \cdot 2^{2} + 1 = 0 : u = \frac{1}{16}

u = \frac{1}{16}

Substitute back

u = 2^{x},

solve for

x

Solve

2^{x} = \frac{1}{16} : x = - 4

x = - 4

(3^{x}) - 54 x + 135 = 0

8 = 2^{x}

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

x, 2^{x} = \frac{( 1 + y )}{( 1 - y )}

\frac{( 5 ^{5} \cdot 5 ^{- 4} \cdot 5 ^{x} )}{( 5 ^{12} )} = 5^{- 5}

What is the answer to 2^{2x+8}-8*2^{x+2}+1=0 ?
The answer to 2^{2x+8}-8*2^{x+2}+1=0 is x=-4
Solve for x: 2^{2x+8}-8*2^{x+2}+1=0
The solution is x=-4