What is the answer to 2^{x/2}+2^x=6 ?

The answer to 2^{x/2}+2^x=6 is x=2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

2^{x/2}+2^x=6

2^{\frac{x}{2}} + 2^{x} = 6

x = 2

Solution steps

2^{\frac{x}{2}} + 2^{x} = 6

Apply exponent rules

(2^{x})^{0.5} + 2^{x} = 6

Rewrite the equation with

2^{x} = u

u^{0.5} + u = 6

Solve

u^{0.5} + u = 6 : u = 4

u = 4

Substitute back

u = 2^{x},

solve for

x

Solve

2^{x} = 4 : x = 2

x = 2

7^{3 x + 1} = e^{x}

3^{x} = 93

4^{2 x + 1} = 1024

x 9 = 243

2^{x} - 2^{x - 1} = 4