Precalculus Examples

$\log_{9} (\frac{x^{5}}{y^{5} z^{7}})$

Step 1

Rewrite $\log_{9} (\frac{x^{5}}{y^{5} z^{7}})$ as $\log_{9} (x^{5}) - \log_{9} (y^{5} z^{7})$ .

$\log_{9} (x^{5}) - \log_{9} (y^{5} z^{7})$

Step 2

Expand $\log_{9} (x^{5})$ by moving $5$ outside the logarithm.

$5 \log_{9} (x) - \log_{9} (y^{5} z^{7})$

Step 3

Rewrite $\log_{9} (y^{5} z^{7})$ as $\log_{9} (y^{5}) + \log_{9} (z^{7})$ .

$5 \log_{9} (x) - (\log_{9} (y^{5}) + \log_{9} (z^{7}))$

Step 4

Expand $\log_{9} (y^{5})$ by moving $5$ outside the logarithm.

$5 \log_{9} (x) - (5 \log_{9} (y) + \log_{9} (z^{7}))$

Step 5

Expand $\log_{9} (z^{7})$ by moving $7$ outside the logarithm.

$5 \log_{9} (x) - (5 \log_{9} (y) + 7 \log_{9} (z))$

Step 6

Simplify each term.

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Step 6.1

Apply the distributive property.

$5 \log_{9} (x) - (5 \log_{9} (y)) - (7 \log_{9} (z))$

Step 6.2

Multiply $5$ by $- 1$ .

$5 \log_{9} (x) - 5 \log_{9} (y) - (7 \log_{9} (z))$

Step 6.3

Multiply $7$ by $- 1$ .

$5 \log_{9} (x) - 5 \log_{9} (y) - 7 \log_{9} (z)$