Precalculus Examples

$\ln (\frac{e^{3}}{x y^{2}})$

Step 1

Rewrite $\ln (\frac{e^{3}}{x y^{2}})$ as $\ln (e^{3}) - \ln (x y^{2})$ .

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

Step 2

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

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

Step 3

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

$3 \cdot 1 - \ln (x y^{2})$

Step 4

Multiply $3$ by $1$ .

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

Step 5

Rewrite $\ln (x y^{2})$ as $\ln (x) + \ln (y^{2})$ .

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

Step 6

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

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

Step 7

Simplify each term.

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Step 7.1

Apply the distributive property.

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

Step 7.2

Multiply $2$ by $- 1$ .

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