Write as a Single Logarithm 5 natural log of x-2- natural log of x+2-3 natural log of x

$5 \ln (x - 2) - \ln (x + 2) - 3 \ln (x)$

Simplify each term.

Simplify $5 \ln (x - 2)$ by moving $5$ inside the logarithm.

$\ln ({(x - 2)}^{5}) - \ln (x + 2) - 3 \ln (x)$

Simplify $- 3 \ln (x)$ by moving $3$ inside the logarithm.

$\ln ({(x - 2)}^{5}) - \ln (x + 2) - \ln (x^{3})$

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

$\ln (\frac{{(x - 2)}^{5}}{x + 2}) - \ln (x^{3})$

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

$\ln (\frac{\frac{{(x - 2)}^{5}}{x + 2}}{x^{3}})$

Multiply the numerator by the reciprocal of the denominator.

$\ln (\frac{{(x - 2)}^{5}}{x + 2} \cdot \frac{1}{x^{3}})$

Multiply $\frac{{(x - 2)}^{5}}{x + 2}$ by $\frac{1}{x^{3}}$ .

$\ln (\frac{{(x - 2)}^{5}}{(x + 2) x^{3}})$

Reorder factors in $\ln (\frac{{(x - 2)}^{5}}{(x + 2) x^{3}})$ .

$\ln (\frac{{(x - 2)}^{5}}{x^{3} (x + 2)})$