Pre-Algebra Examples

$g (x) = \log (x - 2) + \log (2 x - 1)$

Step 1

Simplify and reorder the polynomial.

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Step 1.1

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

$\log ((x - 2) (2 x - 1))$

Step 1.2

Expand $(x - 2) (2 x - 1)$ using the FOIL Method.

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Step 1.2.1

Apply the distributive property.

$\log (x (2 x - 1) - 2 (2 x - 1))$

Step 1.2.2

Apply the distributive property.

$\log (x (2 x) + x \cdot - 1 - 2 (2 x - 1))$

Step 1.2.3

Apply the distributive property.

$\log (x (2 x) + x \cdot - 1 - 2 (2 x) - 2 \cdot - 1)$

Step 1.3

Simplify and combine like terms.

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Step 1.3.1

Simplify each term.

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Step 1.3.1.1

Rewrite using the commutative property of multiplication.

$\log (2 x \cdot x + x \cdot - 1 - 2 (2 x) - 2 \cdot - 1)$

Step 1.3.1.2

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

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Step 1.3.1.2.1

Move $x$ .

$\log (2 (x \cdot x) + x \cdot - 1 - 2 (2 x) - 2 \cdot - 1)$

Step 1.3.1.2.2

Multiply $x$ by $x$ .

$\log (2 x^{2} + x \cdot - 1 - 2 (2 x) - 2 \cdot - 1)$

Step 1.3.1.3

Move $- 1$ to the left of $x$ .

$\log (2 x^{2} - 1 \cdot x - 2 (2 x) - 2 \cdot - 1)$

Step 1.3.1.4

Rewrite $- 1 x$ as $- x$ .

$\log (2 x^{2} - x - 2 (2 x) - 2 \cdot - 1)$

Step 1.3.1.5

Multiply $2$ by $- 2$ .

$\log (2 x^{2} - x - 4 x - 2 \cdot - 1)$

Step 1.3.1.6

Multiply $- 2$ by $- 1$ .

$\log (2 x^{2} - x - 4 x + 2)$

Step 1.3.2

Subtract $4 x$ from $- x$ .

$\log (2 x^{2} - 5 x + 2)$

Step 2

The degree cannot be determined because $\log (2 x^{2} - 5 x + 2)$ is not a polynomial.

Not a polynomial