What is the answer to 3^{2x}-3^{x+2}=3^x-9 ?

The answer to 3^{2x}-3^{x+2}=3^x-9 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 >

3^{2x}-3^{x+2}=3^x-9

3^{2 x} - 3^{x + 2} = 3^{x} - 9

x = 2, x = 0

Solution steps

3^{2 x} - 3^{x + 2} = 3^{x} - 9

Apply exponent rules

(3^{x})^{2} - 3^{x} \cdot 3^{2} = 3^{x} - 9

Rewrite the equation with

3^{x} = u

(u)^{2} - u \cdot 3^{2} = u - 9

Solve

u^{2} - u \cdot 3^{2} = u - 9 : u = 9, u = 1

u = 9, u = 1

Substitute back

u = 3^{x},

solve for

x

Solve

3^{x} = 9 : x = 2

Solve

3^{x} = 1 : x = 0

x = 2, x = 0

2 x e^{x} + e^{x} (x^{2} - 3) = 0

e^{2 x} = 3 e^{- \frac{1}{4} x}

\frac{a ^{20}}{a ^{x}} = a^{3}

x, 3^{1 - 2 x} = 4^{x}

3^{x} = \frac{1}{27}

What is the answer to 3^{2x}-3^{x+2}=3^x-9 ?
The answer to 3^{2x}-3^{x+2}=3^x-9 is x=2,x=0
Solve for x: 3^{2x}-3^{x+2}=3^x-9
The solution is x=2,x=0