Precalculus Examples

$\log_{11} (2) + \log_{11} (x + 6) + \log_{11} (y + 4)$

Step 1

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

$\log_{11} (2 (x + 6)) + \log_{11} (y + 4)$

Step 2

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

$\log_{11} (2 (x + 6) (y + 4))$

Step 3

Simplify by multiplying through.

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Step 3.1

Apply the distributive property.

$\log_{11} ((2 x + 2 \cdot 6) (y + 4))$

Step 3.2

Multiply $2$ by $6$ .

$\log_{11} ((2 x + 12) (y + 4))$

Step 4

Expand $(2 x + 12) (y + 4)$ using the FOIL Method.

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Step 4.1

Apply the distributive property.

$\log_{11} (2 x (y + 4) + 12 (y + 4))$

Step 4.2

Apply the distributive property.

$\log_{11} (2 x y + 2 x \cdot 4 + 12 (y + 4))$

Step 4.3

Apply the distributive property.

$\log_{11} (2 x y + 2 x \cdot 4 + 12 y + 12 \cdot 4)$

Step 5

Simplify each term.

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Step 5.1

Multiply $4$ by $2$ .

$\log_{11} (2 x y + 8 x + 12 y + 12 \cdot 4)$

Step 5.2

Multiply $12$ by $4$ .

$\log_{11} (2 x y + 8 x + 12 y + 48)$