What is the answer to 2^{3y}-2^{2y}-2^{y+1}=0 ?

The answer to 2^{3y}-2^{2y}-2^{y+1}=0 is y=1

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2^{3y}-2^{2y}-2^{y+1}=0

2^{3 y} - 2^{2 y} - 2^{y + 1} = 0

y = 1

Solution steps

2^{3 y} - 2^{2 y} - 2^{y + 1} = 0

Apply exponent rules

(2^{y})^{3} - (2^{y})^{2} - 2^{y} \cdot 2^{1} = 0

Rewrite the equation with

2^{y} = u

(u)^{3} - (u)^{2} - u \cdot 2^{1} = 0

Solve

u^{3} - u^{2} - u \cdot 2^{1} = 0 : u = 0, u = - 1, u = 2

u = 0, u = - 1, u = 2

Substitute back

u = 2^{y},

solve for

y

Solve

2^{y} = 0 :

No Solution for

y \in R

Solve

2^{y} = - 1 :

No Solution for

y \in R

Solve

2^{y} = 2 : y = 1

y = 1

x, ln (y) = e^{x} + ln (2)

u, y = x^{u}

9^{- x - 4} = 27

30 = 80 e^{(- x) (1)}

3^{n + 1} = 2^{n}

What is the answer to 2^{3y}-2^{2y}-2^{y+1}=0 ?
The answer to 2^{3y}-2^{2y}-2^{y+1}=0 is y=1
Solve for y: 2^{3y}-2^{2y}-2^{y+1}=0
The solution is y=1