Precalculus Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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

Step 1.2

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

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

Step 2

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

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

Step 3

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

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

Step 4

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

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Step 4.1

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

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Step 4.1.1

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

$\log (x^{1} x^{2} y^{2})$

Step 4.1.2

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

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

Step 4.2

Add $1$ and $2$ .

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