What is the answer to 1/3 =(2^{|x|-2}-1)^{-1} ?

The answer to 1/3 =(2^{|x|-2}-1)^{-1} is x=-4,x=4

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

1/3 =(2^{|x|-2}-1)^{-1}

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

x = - 4, x = 4

Solution steps

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

Multiply both sides by

3

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

Simplify

(2^{∣ x ∣ - 2} - 1)^{- 1} \cdot 3 : \frac{3}{2 ^{∣ x ∣ - 2} - 1}

1 = \frac{3}{2 ^{∣ x ∣ - 2} - 1}

Rewrite the equation with

2^{∣ x ∣ - 2} = u

1 = \frac{3}{u - 1}

Solve

1 = \frac{3}{u - 1} : u = 4

u = 4

Substitute back

u = 2^{∣ x ∣ - 2},

solve for

x

Solve

2^{∣ x ∣ - 2} = 4 : x = - 4, x = 4

x = - 4, x = 4

Verify Solutions:

x = - 4

True

, x = 4

True

The solutions are

x = - 4, x = 4

3^{- 8}

2 s - 5 \geq 40

3 x - 1 < - 25

(3 x + 5)^{2} - 5 x (x + 10) > 0

i^{- 15}

What is the answer to 1/3 =(2^{|x|-2}-1)^{-1} ?
The answer to 1/3 =(2^{|x|-2}-1)^{-1} is x=-4,x=4
Solve for x: 1/3 =(2^{|x|-2}-1)^{-1}
The solution is x=-4,x=4