What is the answer to 2^{2x-2}-2^{2+(x-1)}=-4 ?

The answer to 2^{2x-2}-2^{2+(x-1)}=-4 is x=2

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2^{2x-2}-2^{2+(x-1)}=-4

2^{2 x - 2} - 2^{2 + (x - 1)} = - 4

x = 2

Solution steps

2^{2 x - 2} - 2^{2 + (x - 1)} = - 4

Apply exponent rules

(2^{x})^{2} \cdot 2^{- 2} - 2^{x} \cdot 2^{1} = - 4

Rewrite the equation with

2^{x} = u

(u)^{2} \cdot 2^{- 2} - u \cdot 2^{1} = - 4

Solve

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

u = 4

Substitute back

u = 2^{x},

solve for

x

Solve

2^{x} = 4 : x = 2

x = 2

e^{x} - \frac{1}{x} = 0

1 - e^{x} = 0

2^{2 x - 1} = 4

4 e^{x + 4} = 3 e^{2 x - 1}

1.04 5^{x} = 2

What is the answer to 2^{2x-2}-2^{2+(x-1)}=-4 ?
The answer to 2^{2x-2}-2^{2+(x-1)}=-4 is x=2
Solve for x: 2^{2x-2}-2^{2+(x-1)}=-4
The solution is x=2