Precalculus Examples

$\ln (\frac{9}{7 x^{7} y})$

Step 1

Rewrite $\ln (\frac{9}{7 x^{7} y})$ as $\ln (9) - \ln (7 x^{7} y)$ .

$\ln (9) - \ln (7 x^{7} y)$

Step 2

Rewrite $\ln (7 x^{7} y)$ as $\ln (7 x^{7}) + \ln (y)$ .

$\ln (9) - (\ln (7 x^{7}) + \ln (y))$

Step 3

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

$\ln (9) - (\ln (7) + \ln (x^{7}) + \ln (y))$

Step 4

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

$\ln (9) - (\ln (7) + 7 \ln (x) + \ln (y))$

Step 5

Simplify each term.

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Step 5.1

Rewrite $\ln (9)$ as $\ln (3^{2})$ .

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

Step 5.2

Expand $\ln (3^{2})$ by moving $2$ outside the logarithm.

$2 \ln (3) - (\ln (7) + 7 \ln (x) + \ln (y))$

Step 5.3

Apply the distributive property.

$2 \ln (3) - \ln (7) - (7 \ln (x)) - \ln (y)$

Step 5.4

Multiply $7$ by $- 1$ .

$2 \ln (3) - \ln (7) - 7 \ln (x) - \ln (y)$