What is the answer to 2^{2x}-10(2^x)+16=0 ?

The answer to 2^{2x}-10(2^x)+16=0 is x=3,x=1

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2^{2x}-10(2^x)+16=0

2^{2 x} - 10 (2^{x}) + 16 = 0

x = 3, x = 1

Solution steps

2^{2 x} - 10 (2^{x}) + 16 = 0

Apply exponent rules

(2^{x})^{2} - 10 \cdot 2^{x} + 16 = 0

Rewrite the equation with

2^{x} = u

(u)^{2} - 10 u + 16 = 0

Solve

u^{2} - 10 u + 16 = 0 : u = 8, u = 2

u = 8, u = 2

Substitute back

u = 2^{x},

solve for

x

Solve

2^{x} = 8 : x = 3

Solve

2^{x} = 2 : x = 1

x = 3, x = 1

e^{x} + e^{- x} = 4

30 = 1 0^{x}

64 \cdot 1 6^{- 3 x} = 1 6^{3 x - 2}

12 5^{2 - 3 x} = 5

3^{x} = 27

What is the answer to 2^{2x}-10(2^x)+16=0 ?
The answer to 2^{2x}-10(2^x)+16=0 is x=3,x=1
Solve for x: 2^{2x}-10(2^x)+16=0
The solution is x=3,x=1