What is the answer to 2^{3x+1}-2^{2x-1}=2^{x+3}-2 ?

The answer to 2^{3x+1}-2^{2x-1}=2^{x+3}-2 is x=1,x=-2

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

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

x = 1, x = - 2

Solution steps

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

Apply exponent rules

(2^{x})^{3} \cdot 2^{1} - (2^{x})^{2} \cdot 2^{- 1} = 2^{x} \cdot 2^{3} - 2

Rewrite the equation with

2^{x} = u

(u)^{3} \cdot 2^{1} - (u)^{2} \cdot 2^{- 1} = u \cdot 2^{3} - 2

Solve

u^{3} \cdot 2^{1} - u^{2} \cdot 2^{- 1} = u \cdot 2^{3} - 2 : u = - 2, u = 2, u = \frac{1}{4}

u = - 2, u = 2, u = \frac{1}{4}

Substitute back

u = 2^{x},

solve for

x

Solve

2^{x} = - 2 :

No Solution for

x \in R

Solve

2^{x} = 2 : x = 1

Solve

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

x = 1, x = - 2

2^{5 x - 2} = 2^{x}

x, e^{x - 3} = 2

(\frac{2}{3})^{x} = 5^{x - 1}

3^{x + 2} + 3^{2 - x} = 82

2 0^{x - 9} = 12

What is the answer to 2^{3x+1}-2^{2x-1}=2^{x+3}-2 ?
The answer to 2^{3x+1}-2^{2x-1}=2^{x+3}-2 is x=1,x=-2
Solve for x: 2^{3x+1}-2^{2x-1}=2^{x+3}-2
The solution is x=1,x=-2