Precalculus Examples

$\ln (\frac{2}{5 x^{5} y})$

Step 1

Rewrite $\ln (\frac{2}{5 x^{5} y})$ as $\ln (2) - \ln (5 x^{5} y)$ .

$\ln (2) - \ln (5 x^{5} y)$

Step 2

Rewrite $\ln (5 x^{5} y)$ as $\ln (5 x^{5}) + \ln (y)$ .

$\ln (2) - (\ln (5 x^{5}) + \ln (y))$

Step 3

Rewrite $\ln (5 x^{5})$ as $\ln (5) + \ln (x^{5})$ .

$\ln (2) - (\ln (5) + \ln (x^{5}) + \ln (y))$

Step 4

Expand $\ln (x^{5})$ by moving $5$ outside the logarithm.

$\ln (2) - (\ln (5) + 5 \ln (x) + \ln (y))$

Step 5

Simplify each term.

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Step 5.1

Apply the distributive property.

$\ln (2) - \ln (5) - (5 \ln (x)) - \ln (y)$

Step 5.2

Multiply $5$ by $- 1$ .

$\ln (2) - \ln (5) - 5 \ln (x) - \ln (y)$