Precalculus Examples

$\log_{4} ({(x y)}^{3}) - \log_{4} (x y)$

Step 1

Use the quotient property of logarithms, $\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

$\log_{4} (\frac{{(x y)}^{3}}{x y})$

Step 2

Apply the product rule to $x y$ .

$\log_{4} (\frac{x^{3} y^{3}}{x y})$

Step 3

Cancel the common factor of $x^{3}$ and $x$ .

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Step 3.1

Factor $x$ out of $x^{3} y^{3}$ .

$\log_{4} (\frac{x (x^{2} y^{3})}{x y})$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $x$ out of $x y$ .

$\log_{4} (\frac{x (x^{2} y^{3})}{x (y)})$

Step 3.2.2

Cancel the common factor.

$\log_{4} (\frac{x (x^{2} y^{3})}{x y})$

Step 3.2.3

Rewrite the expression.

$\log_{4} (\frac{x^{2} y^{3}}{y})$

$\log_{4} (\frac{x^{2} y^{3}}{y})$

$\log_{4} (\frac{x^{2} y^{3}}{y})$

Step 4

Cancel the common factor of $y^{3}$ and $y$ .

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Step 4.1

Factor $y$ out of $x^{2} y^{3}$ .

$\log_{4} (\frac{y (x^{2} y^{2})}{y})$

Step 4.2

Cancel the common factors.

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Step 4.2.1

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

$\log_{4} (\frac{y (x^{2} y^{2})}{y^{1}})$

Step 4.2.2

Factor $y$ out of $y^{1}$ .

$\log_{4} (\frac{y (x^{2} y^{2})}{y \cdot 1})$

Step 4.2.3

Cancel the common factor.

$\log_{4} (\frac{y (x^{2} y^{2})}{y \cdot 1})$

Step 4.2.4

Rewrite the expression.

$\log_{4} (\frac{x^{2} y^{2}}{1})$

Step 4.2.5

Divide $x^{2} y^{2}$ by $1$ .

$\log_{4} (x^{2} y^{2})$

$\log_{4} (x^{2} y^{2})$

$\log_{4} (x^{2} y^{2})$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$