What is the answer to 2^{2x}-3*2^{x+2}+32=0 ?

The answer to 2^{2x}-3*2^{x+2}+32=0 is x=3,x=2

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2^{2x}-3*2^{x+2}+32=0

2^{2 x} - 3 \cdot 2^{x + 2} + 32 = 0

x = 3, x = 2

Solution steps

2^{2 x} - 3 \cdot 2^{x + 2} + 32 = 0

Apply exponent rules

(2^{x})^{2} - 3 \cdot 2^{x} \cdot 2^{2} + 32 = 0

Rewrite the equation with

2^{x} = u

(u)^{2} - 3 u \cdot 2^{2} + 32 = 0

Solve

u^{2} - 3 u \cdot 2^{2} + 32 = 0 : u = 8, u = 4

u = 8, u = 4

Substitute back

u = 2^{x},

solve for

x

Solve

2^{x} = 8 : x = 3

Solve

2^{x} = 4 : x = 2

x = 3, x = 2

1 \cdot 1 0^{x} = 3

4^{x} + 2^{x} = 8

16384 = 2^{x}

3^{x + 2} - 17 \cdot 3^{x - 1} = 30

4860 \cdot 0. 9^{x} = 20

What is the answer to 2^{2x}-3*2^{x+2}+32=0 ?
The answer to 2^{2x}-3*2^{x+2}+32=0 is x=3,x=2
Solve for x: 2^{2x}-3*2^{x+2}+32=0
The solution is x=3,x=2