Precalculus Examples

$\log_{5} (x^{3} y^{3} z)$

Step 1

Rewrite $\log_{5} (x^{3} y^{3} z)$ as $\log_{5} (x^{3} y^{3}) + \log_{5} (z)$ .

$\log_{5} (x^{3} y^{3}) + \log_{5} (z)$

Step 2

Rewrite $\log_{5} (x^{3} y^{3})$ as $\log_{5} (x^{3}) + \log_{5} (y^{3})$ .

$\log_{5} (x^{3}) + \log_{5} (y^{3}) + \log_{5} (z)$

Step 3

Expand $\log_{5} (x^{3})$ by moving $3$ outside the logarithm.

$3 \log_{5} (x) + \log_{5} (y^{3}) + \log_{5} (z)$

Step 4

Expand $\log_{5} (y^{3})$ by moving $3$ outside the logarithm.

$3 \log_{5} (x) + 3 \log_{5} (y) + \log_{5} (z)$