Precalculus Examples

$\log (\frac{x^{3}}{y^{4} z})$

Step 1

Rewrite $\log (\frac{x^{3}}{y^{4} z})$ as $\log (x^{3}) - \log (y^{4} z)$ .

$\log (x^{3}) - \log (y^{4} z)$

Step 2

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

$3 \log (x) - \log (y^{4} z)$

Step 3

Rewrite $\log (y^{4} z)$ as $\log (y^{4}) + \log (z)$ .

$3 \log (x) - (\log (y^{4}) + \log (z))$

Step 4

Expand $\log (y^{4})$ by moving $4$ outside the logarithm.

$3 \log (x) - (4 \log (y) + \log (z))$

Step 5

Simplify each term.

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Step 5.1

Apply the distributive property.

$3 \log (x) - (4 \log (y)) - \log (z)$

Step 5.2

Multiply $4$ by $- 1$ .

$3 \log (x) - 4 \log (y) - \log (z)$