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

The answer to 2^x+4*2^{-x}=5 is x=2,x=0

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

x = 2, x = 0

Solution steps

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

Apply exponent rules

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

Rewrite the equation with

2^{x} = u

u + 4 (u)^{- 1} = 5

Solve

u + 4 u^{- 1} = 5 : u = 4, u = 1

u = 4, u = 1

Substitute back

u = 2^{x},

solve for

x

Solve

2^{x} = 4 : x = 2

Solve

2^{x} = 1 : x = 0

x = 2, x = 0

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

(2 e)^{x^{2} - 2} = 4

24 3^{x + 2} \cdot 9^{2 x - 1} = 9

200 = 100 (1 + \frac{8}{100})^{x}

8^{x - 3} = 6 4^{3 - x}