Precalculus Examples

$\ln (\frac{x^{4} v (p^{9} q^{7})}{e^{8}})$

Step 1

Rewrite $\ln (\frac{x^{4} v (p^{9} q^{7})}{e^{8}})$ as $\ln (x^{4} v (p^{9} q^{7})) - \ln (e^{8})$ .

$\ln (x^{4} v (p^{9} q^{7})) - \ln (e^{8})$

Step 2

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

$\ln (x^{4} v (p^{9} q^{7})) - (8 \ln (e))$

Step 3

The natural logarithm of $e$ is $1$ .

$\ln (x^{4} v (p^{9} q^{7})) - (8 \cdot 1)$

Step 4

Multiply $8$ by $1$ .

$\ln (x^{4} v (p^{9} q^{7})) - 1 \cdot 8$

Step 5

Multiply $- 1$ by $8$ .

$\ln (x^{4} v (p^{9} q^{7})) - 8$

Step 6

Rewrite $\ln (x^{4} v (p^{9} q^{7}))$ as $\ln (x^{4}) + \ln (v (p^{9} q^{7}))$ .

$\ln (x^{4}) + \ln (v (p^{9} q^{7})) - 8$

Step 7

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

$4 \ln (x) + \ln (v (p^{9} q^{7})) - 8$