Precalculus Examples

$\log_{4} (\frac{x y^{6}}{z^{3}})$

Step 1

Rewrite $\log_{4} (\frac{x y^{6}}{z^{3}})$ as $\log_{4} (x y^{6}) - \log_{4} (z^{3})$ .

$\log_{4} (x y^{6}) - \log_{4} (z^{3})$

Step 2

Expand $\log_{4} (z^{3})$ by moving $3$ outside the logarithm.

$\log_{4} (x y^{6}) - (3 \log_{4} (z))$

Step 3

Multiply $3$ by $- 1$ .

$\log_{4} (x y^{6}) - 3 \log_{4} (z)$

Step 4

Rewrite $\log_{4} (x y^{6})$ as $\log_{4} (x) + \log_{4} (y^{6})$ .

$\log_{4} (x) + \log_{4} (y^{6}) - 3 \log_{4} (z)$

Step 5

Expand $\log_{4} (y^{6})$ by moving $6$ outside the logarithm.

$\log_{4} (x) + 6 \log_{4} (y) - 3 \log_{4} (z)$