Precalculus Examples

$\log_{5} (a^{6} b^{- 3} c^{4})$

Step 1

Rewrite $\log_{5} (a^{6} b^{- 3} c^{4})$ as $\log_{5} (a^{6} b^{- 3}) + \log_{5} (c^{4})$ .

$\log_{5} (a^{6} b^{- 3}) + \log_{5} (c^{4})$

Step 2

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

$\log_{5} (a^{6}) + \log_{5} (b^{- 3}) + \log_{5} (c^{4})$

Step 3

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

$6 \log_{5} (a) + \log_{5} (b^{- 3}) + \log_{5} (c^{4})$

Step 4

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

$6 \log_{5} (a) - 3 \log_{5} (b) + \log_{5} (c^{4})$

Step 5

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

$6 \log_{5} (a) - 3 \log_{5} (b) + 4 \log_{5} (c)$