Precalculus Examples

$2 \log_{2} (x) + \log_{2} (x y)$

Step 1

Simplify $2 \log_{2} (x)$ by moving $2$ inside the logarithm.

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

Step 2

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

$\log_{2} (x^{2} (x y))$

Step 3

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

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Step 3.1

Move $x$ .

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

Step 3.2

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

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Step 3.2.1

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

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

Step 3.2.2

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

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

Step 3.3

Add $1$ and $2$ .

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