Algebra Examples

$\ln (- 2 x + 5) + \ln (x + 4) = k$

Step 1

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

$\ln ((- 2 x + 5) (x + 4)) = k$

Step 2

Expand $(- 2 x + 5) (x + 4)$ using the FOIL Method.

Tap for more steps...

Step 2.1

Apply the distributive property.

$\ln (- 2 x (x + 4) + 5 (x + 4)) = k$

Step 2.2

Apply the distributive property.

$\ln (- 2 x \cdot x - 2 x \cdot 4 + 5 (x + 4)) = k$

Step 2.3

Apply the distributive property.

$\ln (- 2 x \cdot x - 2 x \cdot 4 + 5 x + 5 \cdot 4) = k$

Step 3

Simplify and combine like terms.

Tap for more steps...

Step 3.1

Simplify each term.

Tap for more steps...

Step 3.1.1

Multiply $x$ by $x$ by adding the exponents.

Tap for more steps...

Step 3.1.1.1

Move $x$ .

$\ln (- 2 (x \cdot x) - 2 x \cdot 4 + 5 x + 5 \cdot 4) = k$

Step 3.1.1.2

Multiply $x$ by $x$ .

$\ln (- 2 x^{2} - 2 x \cdot 4 + 5 x + 5 \cdot 4) = k$

Step 3.1.2

Multiply $4$ by $- 2$ .

$\ln (- 2 x^{2} - 8 x + 5 x + 5 \cdot 4) = k$

Step 3.1.3

Multiply $5$ by $4$ .

$\ln (- 2 x^{2} - 8 x + 5 x + 20) = k$

Step 3.2

Add $- 8 x$ and $5 x$ .

$\ln (- 2 x^{2} - 3 x + 20) = k$