Precalculus Examples

$\log (\frac{3 x y^{2}}{z^{4}})$

Step 1

Rewrite $\log (\frac{3 x y^{2}}{z^{4}})$ as $\log (3 x y^{2}) - \log (z^{4})$ .

$\log (3 x y^{2}) - \log (z^{4})$

Step 2

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

$\log (3 x y^{2}) - (4 \log (z))$

Step 3

Multiply $4$ by $- 1$ .

$\log (3 x y^{2}) - 4 \log (z)$

Step 4

Rewrite $\log (3 x y^{2})$ as $\log (3 x) + \log (y^{2})$ .

$\log (3 x) + \log (y^{2}) - 4 \log (z)$

Step 5

Rewrite $\log (3 x)$ as $\log (3) + \log (x)$ .

$\log (3) + \log (x) + \log (y^{2}) - 4 \log (z)$

Step 6

Expand $\log (y^{2})$ by moving $2$ outside the logarithm.

$\log (3) + \log (x) + 2 \log (y) - 4 \log (z)$