Precalculus Examples

$\log_{5} (x^{6} y^{- 3} z^{4})$

Step 1

Rewrite $\log_{5} (x^{6} y^{- 3} z^{4})$ as $\log_{5} (x^{6} y^{- 3}) + \log_{5} (z^{4})$ .

$\log_{5} (x^{6} y^{- 3}) + \log_{5} (z^{4})$

Step 2

Rewrite $\log_{5} (x^{6} y^{- 3})$ as $\log_{5} (x^{6}) + \log_{5} (y^{- 3})$ .

$\log_{5} (x^{6}) + \log_{5} (y^{- 3}) + \log_{5} (z^{4})$

Step 3

Expand $\log_{5} (x^{6})$ by moving $6$ outside the logarithm.

$6 \log_{5} (x) + \log_{5} (y^{- 3}) + \log_{5} (z^{4})$

Step 4

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

$6 \log_{5} (x) - 3 \log_{5} (y) + \log_{5} (z^{4})$

Step 5

Expand $\log_{5} (z^{4})$ by moving $4$ outside the logarithm.

$6 \log_{5} (x) - 3 \log_{5} (y) + 4 \log_{5} (z)$