Precalculus Examples

$\ln (\frac{7}{4 x^{4} y})$

Step 1

Rewrite $\ln (\frac{7}{4 x^{4} y})$ as $\ln (7) - \ln (4 x^{4} y)$ .

$\ln (7) - \ln (4 x^{4} y)$

Step 2

Rewrite $\ln (4 x^{4} y)$ as $\ln (4 x^{4}) + \ln (y)$ .

$\ln (7) - (\ln (4 x^{4}) + \ln (y))$

Step 3

Rewrite $\ln (4 x^{4})$ as $\ln (4) + \ln (x^{4})$ .

$\ln (7) - (\ln (4) + \ln (x^{4}) + \ln (y))$

Step 4

Expand $\ln (x^{4})$ by moving $4$ outside the logarithm.

$\ln (7) - (\ln (4) + 4 \ln (x) + \ln (y))$

Step 5

Simplify each term.

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Step 5.1

Simplify each term.

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Step 5.1.1

Rewrite $\ln (4)$ as $\ln (2^{2})$ .

$\ln (7) - (\ln (2^{2}) + 4 \ln (x) + \ln (y))$

Step 5.1.2

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

$\ln (7) - (2 \ln (2) + 4 \ln (x) + \ln (y))$

Step 5.2

Apply the distributive property.

$\ln (7) - (2 \ln (2)) - (4 \ln (x)) - \ln (y)$

Step 5.3

Simplify.

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Step 5.3.1

Multiply $2$ by $- 1$ .

$\ln (7) - 2 \ln (2) - (4 \ln (x)) - \ln (y)$

Step 5.3.2

Multiply $4$ by $- 1$ .

$\ln (7) - 2 \ln (2) - 4 \ln (x) - \ln (y)$