What is the answer to 2^{x+1}+2^{3-x}=17 ?

The answer to 2^{x+1}+2^{3-x}=17 is x=3,x=-1

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

2^{x+1}+2^{3-x}=17

2^{x + 1} + 2^{3 - x} = 17

x = 3, x = - 1

Solution steps

2^{x + 1} + 2^{3 - x} = 17

Apply exponent rules

2^{x} \cdot 2^{1} + (2^{x})^{- 1} \cdot 2^{3} = 17

Rewrite the equation with

2^{x} = u

u \cdot 2^{1} + (u)^{- 1} \cdot 2^{3} = 17

Solve

u \cdot 2^{1} + u^{- 1} \cdot 2^{3} = 17 : u = 8, u = \frac{1}{2}

u = 8, u = \frac{1}{2}

Substitute back

u = 2^{x},

solve for

x

Solve

2^{x} = 8 : x = 3

Solve

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

x = 3, x = - 1

2^{5 x} = 94

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

e^{x} - 5 e^{- x} = 4

3 6^{- 3} = 21 6^{2 x + 2}

2^{2 x} = 1

What is the answer to 2^{x+1}+2^{3-x}=17 ?
The answer to 2^{x+1}+2^{3-x}=17 is x=3,x=-1
Solve for x: 2^{x+1}+2^{3-x}=17
The solution is x=3,x=-1