Precalculus Examples

$4 \log (400)$

Step 1

Rewrite $\log (400)$ as $\log (2^{4} \cdot 5^{2})$ .

$4 \log (2^{4} \cdot 5^{2})$

Step 2

Rewrite $\log (2^{4} \cdot 5^{2})$ as $\log (2^{4}) + \log (5^{2})$ .

$4 (\log (2^{4}) + \log (5^{2}))$

Step 3

Simplify each term.

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Step 3.1

Expand $\log (2^{4})$ by moving $4$ outside the logarithm.

$4 (4 \log (2) + \log (5^{2}))$

Step 3.2

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

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

Step 4

Apply the distributive property.

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

Step 5

Multiply $4$ by $4$ .

$16 \log (2) + 4 (2 \log (5))$

Step 6

Multiply $2$ by $4$ .

$16 \log (2) + 8 \log (5)$