Precalculus Examples

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

Step 1

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

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

Step 2

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

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

Step 3

Multiply $4$ by $- 1$ .

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

Step 4

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

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

Step 5

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

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