Precalculus Examples

$\log (24) - \log (6)$

Step 1

Simplify each term.

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Step 1.1

Rewrite $\log (24)$ as $\log (2^{3} \cdot 3)$ .

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

Step 1.2

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

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

Step 1.3

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

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

Step 1.4

Rewrite $\log (6)$ as $\log (2 (3))$ .

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

Step 1.5

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

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

Step 1.6

Apply the distributive property.

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

Step 2

Subtract $\log (3)$ from $\log (3)$ .

$3 \log (2) + 0 - \log (2)$

Step 3

Add $3 \log (2)$ and $0$ .

$3 \log (2) - \log (2)$

Step 4

Subtract $\log (2)$ from $3 \log (2)$ .

$2 \log (2)$