Precalculus Examples

$\ln (\frac{a^{- 2}}{b^{- 4} c^{5}})$

Step 1

Rewrite $\ln (\frac{a^{- 2}}{b^{- 4} c^{5}})$ as $\ln (a^{- 2}) - \ln (b^{- 4} c^{5})$ .

$\ln (a^{- 2}) - \ln (b^{- 4} c^{5})$

Step 2

Expand $\ln (a^{- 2})$ by moving $- 2$ outside the logarithm.

$- 2 \ln (a) - \ln (b^{- 4} c^{5})$

Step 3

Rewrite $\ln (b^{- 4} c^{5})$ as $\ln (b^{- 4}) + \ln (c^{5})$ .

$- 2 \ln (a) - (\ln (b^{- 4}) + \ln (c^{5}))$

Step 4

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

$- 2 \ln (a) - (- 4 \ln (b) + \ln (c^{5}))$

Step 5

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

$- 2 \ln (a) - (- 4 \ln (b) + 5 \ln (c))$

Step 6

Simplify each term.

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Step 6.1

Apply the distributive property.

$- 2 \ln (a) - (- 4 \ln (b)) - (5 \ln (c))$

Step 6.2

Multiply $- 4$ by $- 1$ .

$- 2 \ln (a) + 4 \ln (b) - (5 \ln (c))$

Step 6.3

Multiply $5$ by $- 1$ .

$- 2 \ln (a) + 4 \ln (b) - 5 \ln (c)$