Precalculus Examples

$\log_{8} (\frac{x^{3}}{y^{3} z^{3}})$

Step 1

Rewrite $\log_{8} (\frac{x^{3}}{y^{3} z^{3}})$ as $\log_{8} (x^{3}) - \log_{8} (y^{3} z^{3})$ .

$\log_{8} (x^{3}) - \log_{8} (y^{3} z^{3})$

Step 2

Expand $\log_{8} (x^{3})$ by moving $3$ outside the logarithm.

$3 \log_{8} (x) - \log_{8} (y^{3} z^{3})$

Step 3

Rewrite $\log_{8} (y^{3} z^{3})$ as $\log_{8} (y^{3}) + \log_{8} (z^{3})$ .

$3 \log_{8} (x) - (\log_{8} (y^{3}) + \log_{8} (z^{3}))$

Step 4

Expand $\log_{8} (y^{3})$ by moving $3$ outside the logarithm.

$3 \log_{8} (x) - (3 \log_{8} (y) + \log_{8} (z^{3}))$

Step 5

Expand $\log_{8} (z^{3})$ by moving $3$ outside the logarithm.

$3 \log_{8} (x) - (3 \log_{8} (y) + 3 \log_{8} (z))$

Step 6

Simplify each term.

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Step 6.1

Apply the distributive property.

$3 \log_{8} (x) - (3 \log_{8} (y)) - (3 \log_{8} (z))$

Step 6.2

Multiply $3$ by $- 1$ .

$3 \log_{8} (x) - 3 \log_{8} (y) - (3 \log_{8} (z))$

Step 6.3

Multiply $3$ by $- 1$ .

$3 \log_{8} (x) - 3 \log_{8} (y) - 3 \log_{8} (z)$