Precalculus Examples

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

Step 1

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

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

Step 2

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

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

Step 3

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

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

Step 4

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

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