What is the answer to 4^{2x}-2*4^{x+1}+16=0 ?

The answer to 4^{2x}-2*4^{x+1}+16=0 is x=1

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

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

x = 1

Solution steps

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

Apply exponent rules

(4^{x})^{2} - 2 \cdot 4^{x} \cdot 4^{1} + 16 = 0

Rewrite the equation with

4^{x} = u

(u)^{2} - 2 u \cdot 4^{1} + 16 = 0

Solve

u^{2} - 2 u \cdot 4^{1} + 16 = 0 : u = 4

u = 4

Substitute back

u = 4^{x},

solve for

x

Solve

4^{x} = 4 : x = 1

x = 1

3^{4 x + 8} = 1

e^{2 x} - e^{x} = 2

9^{x + 6} = 3^{3 x}

\frac{1}{2} = e^{- x}

9 \cdot e^{2 z} = 54

What is the answer to 4^{2x}-2*4^{x+1}+16=0 ?
The answer to 4^{2x}-2*4^{x+1}+16=0 is x=1
Solve for x: 4^{2x}-2*4^{x+1}+16=0
The solution is x=1