Precalculus Examples

$\ln (\frac{x^{3} z^{- 7}}{y^{- 8}})$

Step 1

Rewrite $\ln (\frac{x^{3} z^{- 7}}{y^{- 8}})$ as $\ln (x^{3} z^{- 7}) - \ln (y^{- 8})$ .

$\ln (x^{3} z^{- 7}) - \ln (y^{- 8})$

Step 2

Expand $\ln (y^{- 8})$ by moving $- 8$ outside the logarithm.

$\ln (x^{3} z^{- 7}) - (- 8 \ln (y))$

Step 3

Multiply $- 8$ by $- 1$ .

$\ln (x^{3} z^{- 7}) + 8 \ln (y)$

Step 4

Rewrite $\ln (x^{3} z^{- 7})$ as $\ln (x^{3}) + \ln (z^{- 7})$ .

$\ln (x^{3}) + \ln (z^{- 7}) + 8 \ln (y)$

Step 5

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

$3 \ln (x) + \ln (z^{- 7}) + 8 \ln (y)$

Step 6

Expand $\ln (z^{- 7})$ by moving $- 7$ outside the logarithm.

$3 \ln (x) - 7 \ln (z) + 8 \ln (y)$