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

The answer to 2^{x+1}-2(2^{x-1})=2^{4x} is x=0

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

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

x = 0

Solution steps

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

Apply exponent rules

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

Subtract

(2^{x})^{4}

from both sides

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

Simplify

2 \cdot 2^{x} - 2^{x - 1 + 1} - (2^{x})^{4} = 0

Apply exponent rules

- 2^{x} (2^{x} - 1) (4^{x} + 2^{x} + 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

2^{x} = 0 or 2^{x} - 1 = 0 or 4^{x} + 2^{x} + 1 = 0

Solve

2^{x} = 0 :

No Solution for

x \in R

Solve

2^{x} - 1 = 0 : x = 0

Solve

4^{x} + 2^{x} + 1 = 0 :

No Solution for

x \in R

x = 0

1^{x} = 10

1 - e^{(- 0.75 x)} = 0.4268

4 \cdot 3^{x + 1} - 9^{x} = 27

100 = 200 e^{- 0.06 x}

x^{2} e^{- x} = x e^{- x}

What is the answer to 2^{x+1}-2(2^{x-1})=2^{4x} ?
The answer to 2^{x+1}-2(2^{x-1})=2^{4x} is x=0
Solve for x: 2^{x+1}-2(2^{x-1})=2^{4x}
The solution is x=0