Precalculus Examples

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

Step 1

Use the quotient property of logarithms, $\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

$4 (\ln (\frac{x}{x + 4}) - \ln (x - 4))$

Step 2

Use the quotient property of logarithms, $\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

$4 \ln (\frac{\frac{x}{x + 4}}{x - 4})$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$4 \ln (\frac{x}{x + 4} \cdot \frac{1}{x - 4})$

Step 4

Multiply $\frac{x}{x + 4}$ by $\frac{1}{x - 4}$ .

$4 \ln (\frac{x}{(x + 4) (x - 4)})$

Step 5

Simplify $4 \ln (\frac{x}{(x + 4) (x - 4)})$ by moving $4$ inside the logarithm.

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

Step 6

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 6.1

Apply the product rule to $\frac{x}{(x + 4) (x - 4)}$ .

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

Step 6.2

Apply the product rule to $(x + 4) (x - 4)$ .

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