What is the answer to 2^{2x}-5*2^{x+2}+64=0 ?

The answer to 2^{2x}-5*2^{x+2}+64=0 is x=4,x=2

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2^{2x}-5*2^{x+2}+64=0

2^{2 x} - 5 \cdot 2^{x + 2} + 64 = 0

x = 4, x = 2

Solution steps

2^{2 x} - 5 \cdot 2^{x + 2} + 64 = 0

Apply exponent rules

(2^{x})^{2} - 5 \cdot 2^{x} \cdot 2^{2} + 64 = 0

Rewrite the equation with

2^{x} = u

(u)^{2} - 5 u \cdot 2^{2} + 64 = 0

Solve

u^{2} - 5 u \cdot 2^{2} + 64 = 0 : u = 16, u = 4

u = 16, u = 4

Substitute back

u = 2^{x},

solve for

x

Solve

2^{x} = 16 : x = 4

Solve

2^{x} = 4 : x = 2

x = 4, x = 2

7^{5 x - 2} = 343

4^{x} = \frac{1}{4}

4 (2^{2 x}) = 8 (2^{x}) - 4

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

4^{x^{2}} = 2^{2 x}

What is the answer to 2^{2x}-5*2^{x+2}+64=0 ?
The answer to 2^{2x}-5*2^{x+2}+64=0 is x=4,x=2
Solve for x: 2^{2x}-5*2^{x+2}+64=0
The solution is x=4,x=2