Precalculus Examples

$\log (30) \cdot 4$

Step 1

Rewrite $\log (30)$ as $\log (2 \cdot 3 \cdot 5)$ .

$\log (2 \cdot 3 \cdot 5) \cdot 4$

Step 2

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

$(\log (2 \cdot 3) + \log (5)) \cdot 4$

Step 3

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

$(\log (2) + \log (3) + \log (5)) \cdot 4$

Step 4

Apply the distributive property.

$\log (2) \cdot 4 + \log (3) \cdot 4 + \log (5) \cdot 4$

Step 5

Simplify.

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Step 5.1

Move $4$ to the left of $\log (2)$ .

$4 \cdot \log (2) + \log (3) \cdot 4 + \log (5) \cdot 4$

Step 5.2

Move $4$ to the left of $\log (3)$ .

$4 \cdot \log (2) + 4 \cdot \log (3) + \log (5) \cdot 4$

Step 5.3

Move $4$ to the left of $\log (5)$ .

$4 \cdot \log (2) + 4 \cdot \log (3) + 4 \cdot \log (5)$

Step 6

Multiply $4$ by $\log (5)$ .

$4 \log (2) + 4 \log (3) + 4 \log (5)$