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

The answer to 5^x+5^{-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 >

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

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

x = 0

Solution steps

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

Apply exponent rules

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

Rewrite the equation with

5^{x} = u

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

Solve

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

u = 1

Substitute back

u = 5^{x},

solve for

x

Solve

5^{x} = 1 : x = 0

x = 0

1 - e^{\frac{- x}{50}} = 0.25

5^{2 x} + 5^{x + 1} - 14 = 0

2^{x + 3} - 15 = 2^{1 - x}

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

36 e^{5 - x} - 6^{2 x} = 0