Precalculus Examples

$\log (\frac{y {(y + 1)}^{7} z^{4}}{x})$

Step 1

Rewrite $\log (\frac{y {(y + 1)}^{7} z^{4}}{x})$ as $\log (y {(y + 1)}^{7} z^{4}) - \log (x)$ .

$\log (y {(y + 1)}^{7} z^{4}) - \log (x)$

Step 2

Rewrite $\log (y {(y + 1)}^{7} z^{4})$ as $\log (y {(y + 1)}^{7}) + \log (z^{4})$ .

$\log (y {(y + 1)}^{7}) + \log (z^{4}) - \log (x)$

Step 3

Rewrite $\log (y {(y + 1)}^{7})$ as $\log (y) + \log ({(y + 1)}^{7})$ .

$\log (y) + \log ({(y + 1)}^{7}) + \log (z^{4}) - \log (x)$

Step 4

Expand $\log ({(y + 1)}^{7})$ by moving $7$ outside the logarithm.

$\log (y) + 7 \log (y + 1) + \log (z^{4}) - \log (x)$

Step 5

Expand $\log (z^{4})$ by moving $4$ outside the logarithm.

$\log (y) + 7 \log (y + 1) + 4 \log (z) - \log (x)$