What is the answer to 4^x-12*2^x+32=0 ?

The answer to 4^x-12*2^x+32=0 is x=3,x=2

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4^x-12*2^x+32=0

4^{x} - 12 \cdot 2^{x} + 32 = 0

x = 3, x = 2

Solution steps

4^{x} - 12 \cdot 2^{x} + 32 = 0

Apply exponent rules

(2^{x})^{2} - 12 \cdot 2^{x} + 32 = 0

Rewrite the equation with

2^{x} = u

(u)^{2} - 12 u + 32 = 0

Solve

u^{2} - 12 u + 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

2^{3 x + 1} = 32

e^{x} = 0.5

2^{2 x - 1} = 3^{x + 2}

x, f = (\frac{1}{2})^{x}

8^{x^{2} - x} = 4^{x + 1}

What is the answer to 4^x-12*2^x+32=0 ?
The answer to 4^x-12*2^x+32=0 is x=3,x=2
Solve for x: 4^x-12*2^x+32=0
The solution is x=3,x=2