Algebra Examples

$\log (9 x y^{2}) - \log (27 x y)$

Step 1

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

$\log (\frac{9 x y^{2}}{27 x y})$

Step 2

Cancel the common factor of $9$ and $27$ .

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Step 2.1

Factor $9$ out of $9 x y^{2}$ .

$\log (\frac{9 (x y^{2})}{27 x y})$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $9$ out of $27 x y$ .

$\log (\frac{9 (x y^{2})}{9 (3 x y)})$

Step 2.2.2

Cancel the common factor.

$\log (\frac{9 (x y^{2})}{9 (3 x y)})$

Step 2.2.3

Rewrite the expression.

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

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

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

Step 3

Cancel the common factor of $x$ .

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Step 3.1

Cancel the common factor.

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

Step 3.2

Rewrite the expression.

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

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

Step 4

Cancel the common factor of $y^{2}$ and $y$ .

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Step 4.1

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

$\log (\frac{y \cdot y}{3 y})$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $y$ out of $3 y$ .

$\log (\frac{y \cdot y}{y \cdot 3})$

Step 4.2.2

Cancel the common factor.

$\log (\frac{y \cdot y}{y \cdot 3})$

Step 4.2.3

Rewrite the expression.

$\log (\frac{y}{3})$

$\log (\frac{y}{3})$

$\log (\frac{y}{3})$

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