Algebra Examples

$2 \log (x) + \log (x + 2)$

Step 1

Simplify $2 \log (x)$ by moving $2$ inside the logarithm.

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

Step 2

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

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

Step 3

Apply the distributive property.

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

Step 4

Multiply $x^{2}$ by $x$ by adding the exponents.

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Step 4.1

Multiply $x^{2}$ by $x$ .

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Step 4.1.1

Raise $x$ to the power of $1$ .

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

Step 4.1.2

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

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

Step 4.2

Add $2$ and $1$ .

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

Step 5

Move $2$ to the left of $x^{2}$ .

$\log (x^{3} + 2 x^{2})$