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

The answer to 2^x+2^{-x}=2 is x=0

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

x = 0

Solution steps

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

Apply exponent rules

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

Rewrite the equation with

2^{x} = u

u + (u)^{- 1} = 2

Solve

u + u^{- 1} = 2 : u = 1

u = 1

Substitute back

u = 2^{x},

solve for

x

Solve

2^{x} = 1 : x = 0

x = 0

5 e^{3 x - 4} = 25

32 \cdot e^{- 0.25 x} = 4

- 14 + 3 e^{x} = 11

5 \cdot 2^{- 3 t} = 45

e^{5 x} = 6 e^{x}