Precalculus Examples

$\log_{5} (\frac{12 a}{2})$

Step 1

Rewrite $\log_{5} (\frac{12 a}{2})$ as $\log_{5} (12 a) - \log_{5} (2)$ .

$\log_{5} (12 a) - \log_{5} (2)$

Step 2

Rewrite $\log_{5} (12 a)$ as $\log_{5} (12) + \log_{5} (a)$ .

$\log_{5} (12) + \log_{5} (a) - \log_{5} (2)$

Step 3

Simplify each term.

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Step 3.1

Rewrite $\log_{5} (12)$ as $\log_{5} (2^{2} \cdot 3)$ .

$\log_{5} (2^{2} \cdot 3) + \log_{5} (a) - \log_{5} (2)$

Step 3.2

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

$\log_{5} (2^{2}) + \log_{5} (3) + \log_{5} (a) - \log_{5} (2)$

Step 3.3

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

$2 \log_{5} (2) + \log_{5} (3) + \log_{5} (a) - \log_{5} (2)$

Step 4

Subtract $\log_{5} (2)$ from $2 \log_{5} (2)$ .

$\log_{5} (2) + \log_{5} (3) + \log_{5} (a)$