Precalculus Examples

$\log_{2} (\frac{x^{5}}{y z})$

Step 1

Rewrite $\log_{2} (\frac{x^{5}}{y z})$ as $\log_{2} (x^{5}) - \log_{2} (y z)$ .

$\log_{2} (x^{5}) - \log_{2} (y z)$

Step 2

Expand $\log_{2} (x^{5})$ by moving $5$ outside the logarithm.

$5 \log_{2} (x) - \log_{2} (y z)$

Step 3

Rewrite $\log_{2} (y z)$ as $\log_{2} (y) + \log_{2} (z)$ .

$5 \log_{2} (x) - (\log_{2} (y) + \log_{2} (z))$

Step 4

Apply the distributive property.

$5 \log_{2} (x) - \log_{2} (y) - \log_{2} (z)$