Precalculus Examples

$\log_{4} (\frac{y z^{2}}{x^{4}})$

Step 1

Rewrite $\log_{4} (\frac{y z^{2}}{x^{4}})$ as $\log_{4} (y z^{2}) - \log_{4} (x^{4})$ .

$\log_{4} (y z^{2}) - \log_{4} (x^{4})$

Step 2

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

$\log_{4} (y z^{2}) - (4 \log_{4} (x))$

Step 3

Multiply $4$ by $- 1$ .

$\log_{4} (y z^{2}) - 4 \log_{4} (x)$

Step 4

Rewrite $\log_{4} (y z^{2})$ as $\log_{4} (y) + \log_{4} (z^{2})$ .

$\log_{4} (y) + \log_{4} (z^{2}) - 4 \log_{4} (x)$

Step 5

Expand $\log_{4} (z^{2})$ by moving $2$ outside the logarithm.

$\log_{4} (y) + 2 \log_{4} (z) - 4 \log_{4} (x)$