What is the answer to 16^x-12*4^x+32=0 ?

The answer to 16^x-12*4^x+32=0 is x= 3/2 ,x=1

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

1 6^{x} - 12 \cdot 4^{x} + 32 = 0

x = \frac{3}{2}, x = 1

Solution steps

1 6^{x} - 12 \cdot 4^{x} + 32 = 0

Apply exponent rules

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

Rewrite the equation with

4^{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 = 4^{x},

solve for

x

Solve

4^{x} = 8 : x = \frac{3}{2}

Solve

4^{x} = 4 : x = 1

x = \frac{3}{2}, x = 1

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

- 3 e^{2 x} + 16 = 5

4^{2 x + 1} = 32

417 e^{x} = 3888

What is the answer to 16^x-12*4^x+32=0 ?
The answer to 16^x-12*4^x+32=0 is x= 3/2 ,x=1
Solve for x: 16^x-12*4^x+32=0
The solution is x= 3/2 ,x=1