Precalculus Examples

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

Step 1

Rewrite $\log (\frac{3^{2} x}{4 y})$ as $\log (3^{2} x) - \log (4 y)$ .

$\log (3^{2} x) - \log (4 y)$

Step 2

Rewrite $\log (3^{2} x)$ as $\log (3^{2}) + \log (x)$ .

$\log (3^{2}) + \log (x) - \log (4 y)$

Step 3

Expand $\log (3^{2})$ by moving $2$ outside the logarithm.

$2 \log (3) + \log (x) - \log (4 y)$

Step 4

Rewrite $\log (4 y)$ as $\log (4) + \log (y)$ .

$2 \log (3) + \log (x) - (\log (4) + \log (y))$

Step 5

Simplify each term.

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Step 5.1

Simplify each term.

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Step 5.1.1

Rewrite $\log (4)$ as $\log (2^{2})$ .

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

Step 5.1.2

Expand $\log (2^{2})$ by moving $2$ outside the logarithm.

$2 \log (3) + \log (x) - (2 \log (2) + \log (y))$

Step 5.2

Apply the distributive property.

$2 \log (3) + \log (x) - (2 \log (2)) - \log (y)$

Step 5.3

Multiply $2$ by $- 1$ .

$2 \log (3) + \log (x) - 2 \log (2) - \log (y)$