Precalculus Examples

$\log_{a} (\frac{m n q}{p^{2} t^{4}})$

Step 1

Rewrite $\log_{a} (\frac{m n q}{p^{2} t^{4}})$ as $\log_{a} (m n q) - \log_{a} (p^{2} t^{4})$ .

$\log_{a} (m n q) - \log_{a} (p^{2} t^{4})$

Step 2

Rewrite $\log_{a} (m n q)$ as $\log_{a} (m n) + \log_{a} (q)$ .

$\log_{a} (m n) + \log_{a} (q) - \log_{a} (p^{2} t^{4})$

Step 3

Rewrite $\log_{a} (m n)$ as $\log_{a} (m) + \log_{a} (n)$ .

$\log_{a} (m) + \log_{a} (n) + \log_{a} (q) - \log_{a} (p^{2} t^{4})$

Step 4

Rewrite $\log_{a} (p^{2} t^{4})$ as $\log_{a} (p^{2}) + \log_{a} (t^{4})$ .

$\log_{a} (m) + \log_{a} (n) + \log_{a} (q) - (\log_{a} (p^{2}) + \log_{a} (t^{4}))$

Step 5

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

$\log_{a} (m) + \log_{a} (n) + \log_{a} (q) - (2 \log_{a} (p) + \log_{a} (t^{4}))$

Step 6

Expand $\log_{a} (t^{4})$ by moving $4$ outside the logarithm.

$\log_{a} (m) + \log_{a} (n) + \log_{a} (q) - (2 \log_{a} (p) + 4 \log_{a} (t))$

Step 7

Simplify each term.

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Step 7.1

Apply the distributive property.

$\log_{a} (m) + \log_{a} (n) + \log_{a} (q) - (2 \log_{a} (p)) - (4 \log_{a} (t))$

Step 7.2

Multiply $2$ by $- 1$ .

$\log_{a} (m) + \log_{a} (n) + \log_{a} (q) - 2 \log_{a} (p) - (4 \log_{a} (t))$

Step 7.3

Multiply $4$ by $- 1$ .

$\log_{a} (m) + \log_{a} (n) + \log_{a} (q) - 2 \log_{a} (p) - 4 \log_{a} (t)$