What is the answer to 1+9^X=3^{X+1}+3^{X-1} ?

The answer to 1+9^X=3^{X+1}+3^{X-1} is X=1,X=-1

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

1+9^X=3^{X+1}+3^{X-1}

1 + 9^{X} = 3^{X + 1} + 3^{X - 1}

X = 1, X = - 1

Solution steps

1 + 9^{X} = 3^{X + 1} + 3^{X - 1}

Simplify

3^{X + 1} + 3^{X - 1} : 10 \cdot 3^{X - 1}

1 + 9^{X} = 10 \cdot 3^{X - 1}

Apply exponent rules

1 + (3^{X})^{2} = 10 \cdot 3^{X} \cdot 3^{- 1}

Rewrite the equation with

3^{X} = u

1 + (u)^{2} = 10 u \cdot 3^{- 1}

Solve

1 + u^{2} = 10 u \cdot 3^{- 1} : u = 3, u = \frac{1}{3}

u = 3, u = \frac{1}{3}

Substitute back

u = 3^{X},

solve for

X

Solve

3^{X} = 3 : X = 1

Solve

3^{X} = \frac{1}{3} : X = - 1

X = 1, X = - 1

2^{3 x + 4} = 2^{2 x}

2^{x} = 8^{3}

2^{x + 1} = 1024

100 e^{x l n (4)} = 50

2^{x + 1} = 13

What is the answer to 1+9^X=3^{X+1}+3^{X-1} ?
The answer to 1+9^X=3^{X+1}+3^{X-1} is X=1,X=-1
Solve for X: 1+9^X=3^{X+1}+3^{X-1}
The solution is X=1,X=-1