Precalculus Examples

$\log_{6} (\frac{r^{2}}{s^{5} t})$

Step 1

Rewrite $\log_{6} (\frac{r^{2}}{s^{5} t})$ as $\log_{6} (r^{2}) - \log_{6} (s^{5} t)$ .

$\log_{6} (r^{2}) - \log_{6} (s^{5} t)$

Step 2

Expand $\log_{6} (r^{2})$ by moving $2$ outside the logarithm.

$2 \log_{6} (r) - \log_{6} (s^{5} t)$

Step 3

Rewrite $\log_{6} (s^{5} t)$ as $\log_{6} (s^{5}) + \log_{6} (t)$ .

$2 \log_{6} (r) - (\log_{6} (s^{5}) + \log_{6} (t))$

Step 4

Expand $\log_{6} (s^{5})$ by moving $5$ outside the logarithm.

$2 \log_{6} (r) - (5 \log_{6} (s) + \log_{6} (t))$

Step 5

Simplify each term.

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Step 5.1

Apply the distributive property.

$2 \log_{6} (r) - (5 \log_{6} (s)) - \log_{6} (t)$

Step 5.2

Multiply $5$ by $- 1$ .

$2 \log_{6} (r) - 5 \log_{6} (s) - \log_{6} (t)$