What is the answer to 9^x+2(3^x)=3^{x+2}-12 ?

The answer to 9^x+2(3^x)=3^{x+2}-12 is x=(2ln(2))/(ln(3)),x=1

Solve for x: 9^x+2(3^x)=3^{x+2}-12

The solution is x=(2ln(2))/(ln(3)),x=1

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

9^{x} + 2 (3^{x}) = 3^{x + 2} - 12

x = \frac{2 ln ( 2 )}{ln ( 3 )}, x = 1

Solution steps

9^{x} + 2 (3^{x}) = 3^{x + 2} - 12

Apply exponent rules

(3^{x})^{2} + 2 \cdot 3^{x} = 3^{x} \cdot 3^{2} - 12

Rewrite the equation with

3^{x} = u

(u)^{2} + 2 u = u \cdot 3^{2} - 12

Solve

u^{2} + 2 u = u \cdot 3^{2} - 12 : u = 4, u = 3

u = 4, u = 3

Substitute back

u = 3^{x},

solve for

x

Solve

3^{x} = 4 : x = \frac{2 ln ( 2 )}{ln ( 3 )}

Solve

3^{x} = 3 : x = 1

x = \frac{2 ln ( 2 )}{ln ( 3 )}, x = 1

1000000 = 2^{n}

3^{3 x} + 3 = 6561

2^{2 x + 1} + 4^{x - 1} = 9

t, e^{t} = x^{2}

8^{x - 2} = 6^{3 x}

What is the answer to 9^x+2(3^x)=3^{x+2}-12 ?
The answer to 9^x+2(3^x)=3^{x+2}-12 is x=(2ln(2))/(ln(3)),x=1
Solve for x: 9^x+2(3^x)=3^{x+2}-12
The solution is x=(2ln(2))/(ln(3)),x=1