What is the answer to 2^{x+2}+7= 1/(2^{x-1)} ?

The answer to 2^{x+2}+7= 1/(2^{x-1)} is x=-2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

2^{x+2}+7= 1/(2^{x-1)}

2^{x + 2} + 7 = \frac{1}{2 ^{x - 1}}

x = - 2

Solution steps

2^{x + 2} + 7 = \frac{1}{2 ^{x - 1}}

Apply exponent rules

2^{x} \cdot 2^{2} + 7 = (2^{x})^{- 1} \cdot 2^{1}

Rewrite the equation with

2^{x} = u

u \cdot 2^{2} + 7 = (u)^{- 1} \cdot 2^{1}

Solve

u \cdot 2^{2} + 7 = u^{- 1} \cdot 2^{1} : u = \frac{1}{4}, u = - 2

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

Substitute back

u = 2^{x},

solve for

x

Solve

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

Solve

2^{x} = - 2 :

No Solution for

x \in R

x = - 2

Verify Solutions:

x = - 2

True

The solution is

x = - 2

2^{- x} = 16

2^{x} = 15

2^{x} = 11

2^{x} = 13

3^{x} (3^{x} - 27) = 0

What is the answer to 2^{x+2}+7= 1/(2^{x-1)} ?
The answer to 2^{x+2}+7= 1/(2^{x-1)} is x=-2
Solve for x: 2^{x+2}+7= 1/(2^{x-1)}
The solution is x=-2