Precalculus Examples

$\frac{1}{7} \cdot (\log_{19} (6 - 2) \log_{19} (n)) - \log_{19} (m)$

Step 1

Subtract $2$ from $6$ .

$\frac{1}{7} \cdot (\log_{19} (4) \log_{19} (n)) - \log_{19} (m)$

Step 2

Simplify each term.

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Step 2.1

Rewrite $\log_{19} (4)$ as $\log_{19} (2^{2})$ .

$\frac{1}{7} \cdot (\log_{19} (2^{2}) \log_{19} (n)) - \log_{19} (m)$

Step 2.2

Expand $\log_{19} (2^{2})$ by moving $2$ outside the logarithm.

$\frac{1}{7} \cdot (2 \log_{19} (2) \log_{19} (n)) - \log_{19} (m)$

Step 2.3

Multiply $\frac{1}{7} (2 \log_{19} (2) \log_{19} (n))$ .

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Step 2.3.1

Combine $2$ and $\frac{1}{7}$ .

$\frac{2}{7} (\log_{19} (2) \log_{19} (n)) - \log_{19} (m)$

Step 2.3.2

Combine $\log_{19} (2)$ and $\frac{2}{7}$ .

$\frac{\log_{19} (2) \cdot 2}{7} \log_{19} (n) - \log_{19} (m)$

Step 2.3.3

Combine $\frac{\log_{19} (2) \cdot 2}{7}$ and $\log_{19} (n)$ .

$\frac{\log_{19} (2) \cdot 2 \log_{19} (n)}{7} - \log_{19} (m)$

Step 2.4

Move $2$ to the left of $\log_{19} (2)$ .

$\frac{2 \log_{19} (2) \log_{19} (n)}{7} - \log_{19} (m)$