What is the answer to 4^x-8*2^x=2^{x-2}-2 ?

The answer to 4^x-8*2^x=2^{x-2}-2 is x=3,x=-2

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4^x-8*2^x=2^{x-2}-2

4^{x} - 8 \cdot 2^{x} = 2^{x - 2} - 2

x = 3, x = - 2

Solution steps

4^{x} - 8 \cdot 2^{x} = 2^{x - 2} - 2

Apply exponent rules

(2^{x})^{2} - 8 \cdot 2^{x} = 2^{x} \cdot 2^{- 2} - 2

Rewrite the equation with

2^{x} = u

(u)^{2} - 8 u = u \cdot 2^{- 2} - 2

Solve

u^{2} - 8 u = u \cdot 2^{- 2} - 2 : u = 8, u = \frac{1}{4}

u = 8, u = \frac{1}{4}

Substitute back

u = 2^{x},

solve for

x

Solve

2^{x} = 8 : x = 3

Solve

2^{x} = \frac{1}{4} : x = - 2

x = 3, x = - 2

8^{x + 1} - 2^{3 x - 1} = 120

(- 1)^{m} = 1

2^{2 x + 8} - 8 \cdot 2^{x + 2} + 1 = 0

(3^{x}) - 54 x + 135 = 0

8 = 2^{x}

What is the answer to 4^x-8*2^x=2^{x-2}-2 ?
The answer to 4^x-8*2^x=2^{x-2}-2 is x=3,x=-2
Solve for x: 4^x-8*2^x=2^{x-2}-2
The solution is x=3,x=-2