What is the answer to 4^x+4^{-x}= 5/2 ?

The answer to 4^x+4^{-x}= 5/2 is x= 1/2 ,x=-1/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

4^x+4^{-x}= 5/2

4^{x} + 4^{- x} = \frac{5}{2}

x = \frac{1}{2}, x = - \frac{1}{2}

Decimal Notation

x = 0.5, x = - 0.5

Solution steps

4^{x} + 4^{- x} = \frac{5}{2}

Apply exponent rules

4^{x} + (4^{x})^{- 1} = \frac{5}{2}

Rewrite the equation with

4^{x} = u

u + (u)^{- 1} = \frac{5}{2}

Solve

u + u^{- 1} = \frac{5}{2} : u = 2, u = \frac{1}{2}

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

Substitute back

u = 4^{x},

solve for

x

Solve

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

Solve

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

x = \frac{1}{2}, x = - \frac{1}{2}

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

2^{x} = \frac{1}{16}

10 0^{x - 1} = 100 0^{2 x}

4^{x} = 1

4^{x} = 3

What is the answer to 4^x+4^{-x}= 5/2 ?
The answer to 4^x+4^{-x}= 5/2 is x= 1/2 ,x=-1/2
Solve for x: 4^x+4^{-x}= 5/2
The solution is x= 1/2 ,x=-1/2