Precalculus Examples

$\log (\frac{z x^{3} {(z + 2)}^{7}}{y^{2}})$

Step 1

Rewrite $\log (\frac{z x^{3} {(z + 2)}^{7}}{y^{2}})$ as $\log (z x^{3} {(z + 2)}^{7}) - \log (y^{2})$ .

$\log (z x^{3} {(z + 2)}^{7}) - \log (y^{2})$

Step 2

Expand $\log (y^{2})$ by moving $2$ outside the logarithm.

$\log (z x^{3} {(z + 2)}^{7}) - (2 \log (y))$

Step 3

Multiply $2$ by $- 1$ .

$\log (z x^{3} {(z + 2)}^{7}) - 2 \log (y)$

Step 4

Rewrite $\log (z x^{3} {(z + 2)}^{7})$ as $\log (z x^{3}) + \log ({(z + 2)}^{7})$ .

$\log (z x^{3}) + \log ({(z + 2)}^{7}) - 2 \log (y)$

Step 5

Rewrite $\log (z x^{3})$ as $\log (z) + \log (x^{3})$ .

$\log (z) + \log (x^{3}) + \log ({(z + 2)}^{7}) - 2 \log (y)$

Step 6

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

$\log (z) + 3 \log (x) + \log ({(z + 2)}^{7}) - 2 \log (y)$

Step 7

Expand $\log ({(z + 2)}^{7})$ by moving $7$ outside the logarithm.

$\log (z) + 3 \log (x) + 7 \log (z + 2) - 2 \log (y)$