Algebra Examples

$\ln (72 x) - 2 \ln (2 y)$

Step 1

Simplify each term.

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Step 1.1

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

$\ln (72 x) - \ln ({(2 y)}^{2})$

Step 1.2

Apply the product rule to $2 y$ .

$\ln (72 x) - \ln (2^{2} y^{2})$

Step 1.3

Raise $2$ to the power of $2$ .

$\ln (72 x) - \ln (4 y^{2})$

Step 2

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

$\ln (\frac{72 x}{4 y^{2}})$

Step 3

Cancel the common factor of $72$ and $4$ .

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Step 3.1

Factor $4$ out of $72 x$ .

$\ln (\frac{4 (18 x)}{4 y^{2}})$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $4$ out of $4 y^{2}$ .

$\ln (\frac{4 (18 x)}{4 (y^{2})})$

Step 3.2.2

Cancel the common factor.

$\ln (\frac{4 (18 x)}{4 y^{2}})$

Step 3.2.3

Rewrite the expression.

$\ln (\frac{18 x}{y^{2}})$