Precalculus Examples

$\log_{11} (a b^{- 4} c^{12} d^{7})$

Step 1

Rewrite $\log_{11} (a b^{- 4} c^{12} d^{7})$ as $\log_{11} (a b^{- 4} c^{12}) + \log_{11} (d^{7})$ .

$\log_{11} (a b^{- 4} c^{12}) + \log_{11} (d^{7})$

Step 2

Rewrite $\log_{11} (a b^{- 4} c^{12})$ as $\log_{11} (a b^{- 4}) + \log_{11} (c^{12})$ .

$\log_{11} (a b^{- 4}) + \log_{11} (c^{12}) + \log_{11} (d^{7})$

Step 3

Rewrite $\log_{11} (a b^{- 4})$ as $\log_{11} (a) + \log_{11} (b^{- 4})$ .

$\log_{11} (a) + \log_{11} (b^{- 4}) + \log_{11} (c^{12}) + \log_{11} (d^{7})$

Step 4

Expand $\log_{11} (b^{- 4})$ by moving $- 4$ outside the logarithm.

$\log_{11} (a) - 4 \log_{11} (b) + \log_{11} (c^{12}) + \log_{11} (d^{7})$

Step 5

Expand $\log_{11} (c^{12})$ by moving $12$ outside the logarithm.

$\log_{11} (a) - 4 \log_{11} (b) + 12 \log_{11} (c) + \log_{11} (d^{7})$

Step 6

Expand $\log_{11} (d^{7})$ by moving $7$ outside the logarithm.

$\log_{11} (a) - 4 \log_{11} (b) + 12 \log_{11} (c) + 7 \log_{11} (d)$