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=-2.01667…,x=2.14313…

Solve for x: 2^{3x-1}-2^{2x-1}=2^{x+3}-2

The solution is x=-2.01667…,x=2.14313…

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

x = - 2.01667 \dots, x = 2.14313 \dots

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 \approx 0.24712 \dots, u \approx - 3.66432 \dots, u \approx 4.41719 \dots

u \approx 0.24712 \dots, u \approx - 3.66432 \dots, u \approx 4.41719 \dots

Substitute back

u = 2^{x},

solve for

x

Solve

2^{x} = 0.24712 \dots : x = - 2.01667 \dots

Solve

2^{x} = - 3.66432 \dots :

No Solution for

x \in R

Solve

2^{x} = 4.41719 \dots : x = 2.14313 \dots

x = - 2.01667 \dots, x = 2.14313 \dots

e^{3 x} = \frac{1}{8}

3 (4^{x}) = (2)^{3 x - 5}

0. 5^{\frac{9900}{x}} = 30

3 \cdot 5^{(x + 1)} = 7 \cdot 4^{x}

3^{4 x} = 2 7^{x + 3}

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=-2.01667…,x=2.14313…
Solve for x: 2^{3x-1}-2^{2x-1}=2^{x+3}-2
The solution is x=-2.01667…,x=2.14313…