Precalculus Examples

$6 \log (36 x^{3})$

Step 1

Rewrite $\log (36 x^{3})$ as $\log (36) + \log (x^{3})$ .

$6 (\log (36) + \log (x^{3}))$

Step 2

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

$6 (\log (36) + 3 \log (x))$

Step 3

Simplify each term.

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Step 3.1

Rewrite $\log (36)$ as $\log (2^{2} \cdot 3^{2})$ .

$6 (\log (2^{2} \cdot 3^{2}) + 3 \log (x))$

Step 3.2

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

$6 (\log (2^{2}) + \log (3^{2}) + 3 \log (x))$

Step 3.3

Simplify each term.

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Step 3.3.1

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

$6 (2 \log (2) + \log (3^{2}) + 3 \log (x))$

Step 3.3.2

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

$6 (2 \log (2) + 2 \log (3) + 3 \log (x))$

Step 4

Apply the distributive property.

$6 (2 \log (2)) + 6 (2 \log (3)) + 6 (3 \log (x))$

Step 5

Simplify.

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Step 5.1

Multiply $2$ by $6$ .

$12 \log (2) + 6 (2 \log (3)) + 6 (3 \log (x))$

Step 5.2

Multiply $2$ by $6$ .

$12 \log (2) + 12 \log (3) + 6 (3 \log (x))$

Step 5.3

Multiply $3$ by $6$ .

$12 \log (2) + 12 \log (3) + 18 \log (x)$