Precalculus Examples

$\log (225) \cdot 15$

Step 1

Rewrite $\log (225)$ as $\log (3^{2} \cdot 5^{2})$ .

$\log (3^{2} \cdot 5^{2}) \cdot 15$

Step 2

Rewrite $\log (3^{2} \cdot 5^{2})$ as $\log (3^{2}) + \log (5^{2})$ .

$(\log (3^{2}) + \log (5^{2})) \cdot 15$

Step 3

Simplify each term.

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Step 3.1

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

$(2 \log (3) + \log (5^{2})) \cdot 15$

Step 3.2

Expand $\log (5^{2})$ by moving $2$ outside the logarithm.

$(2 \log (3) + 2 \log (5)) \cdot 15$

Step 4

Apply the distributive property.

$2 \log (3) \cdot 15 + 2 \log (5) \cdot 15$

Step 5

Multiply $15$ by $2$ .

$30 \log (3) + 2 \log (5) \cdot 15$

Step 6

Multiply $15$ by $2$ .

$30 \log (3) + 30 \log (5)$