Precalculus Examples

$\log (4) + \log (250)$

Step 1

Simplify each term.

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Step 1.1

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

$\log (2^{2}) + \log (250)$

Step 1.2

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

$2 \log (2) + \log (250)$

Step 1.3

Rewrite $\log (250)$ as $\log (2 \cdot 5^{3})$ .

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

Step 1.4

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

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

Step 1.5

Expand $\log (5^{3})$ by moving $3$ outside the logarithm.

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

Step 2

Add $2 \log (2)$ and $\log (2)$ .

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