Write in Standard Form log base 4 of x+6+ log base 4 of x+3=1

$\log_{4} (x + 6) + \log_{4} (x + 3) = 1$

Step 1

Subtract $1$ from both sides of the equation.

$\log_{4} (x + 6) + \log_{4} (x + 3) - 1 = 0$

Step 2

Simplify $\log_{4} (x + 6) + \log_{4} (x + 3) - 1$ .

Use the product property of logarithms, $\log_{b} (x) + \log_{b} (y) = \log_{b} (x y)$ .

$\log_{4} ((x + 6) (x + 3)) - 1 = 0$

Simplify each term.

Expand $(x + 6) (x + 3)$ using the FOIL Method.

Apply the distributive property.

$\log_{4} (x (x + 3) + 6 (x + 3)) - 1 = 0$

Apply the distributive property.

$\log_{4} (x \cdot x + x \cdot 3 + 6 (x + 3)) - 1 = 0$

Apply the distributive property.

$\log_{4} (x \cdot x + x \cdot 3 + 6 x + 6 \cdot 3) - 1 = 0$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$\log_{4} (x^{2} + x \cdot 3 + 6 x + 6 \cdot 3) - 1 = 0$

Move $3$ to the left of $x$ .

$\log_{4} (x^{2} + 3 \cdot x + 6 x + 6 \cdot 3) - 1 = 0$

Multiply $6$ by $3$ .

$\log_{4} (x^{2} + 3 x + 6 x + 18) - 1 = 0$

Add $3 x$ and $6 x$ .

$\log_{4} (x^{2} + 9 x + 18) - 1 = 0$

Step 3

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$a x^{2} + b x + c = 0$

Step 4

The standard form is $\log_{4} (x^{2} + 9 x + 18) - 1$ .

$\log_{4} (x^{2} + 9 x + 18) - 1 = 0$

Step 5