Write as a Function of x 9^x*3^(x+2)=3^(f(x))

$9^{x} \cdot 3^{x + 2} = 3^{f (x)}$

Step 1

Rewrite the equation as $3^{f (x)} = 9^{x} \cdot 3^{x + 2}$ .

$3^{f (x)} = 9^{x} \cdot 3^{x + 2}$

Step 2

Multiply $9^{x} \cdot 3^{x + 2}$ .

Rewrite $9$ as $3^{2}$ .

$3^{f (x)} = {(3^{2})}^{x} \cdot 3^{x + 2}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$3^{f (x)} = 3^{2 x} \cdot 3^{x + 2}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$3^{f (x)} = 3^{2 x + x + 2}$

Add $2 x$ and $x$ .

$3^{f (x)} = 3^{3 x + 2}$

Step 3

Subtract $3^{f (x)}$ from both sides of the equation.

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

Step 4

Rewrite the equation as $3^{3 x + 2} - 3^{f (x)} = 0$ .

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