Identify Expression: Identify the expression inside the logarithm. Calculation: (x-2)/(x+2)Apply Logarithmic Property: Apply the logarithmic property: ln(a/b) = ln(a) - ln(b). Calculation: ln(x-2) - ln(x+2)Check Domain Restrictions: Check for domain restrictions to avoid math errors. Calculation: x-2 and x+2 must not be zero or negative for the logarithm to be defined. x-2 > 0 → x > 2 x+2 > 0 → x > -2 Combined domain: x > 2

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$y=\ln \frac{x-2}{x+2}$

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Precalculus

Evaluate rational exponents

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y=\ln \frac{x-2}{x+2}

Identify Expression: Identify the expression inside the logarithm. $\newline$ Calculation: $(x-2)/(x+2)$
Apply Logarithmic Property: Apply the logarithmic property: $\ln\left(\frac{a}{b}\right) = \ln(a) - \ln(b)$ . $\newline$ Calculation: $\ln(x-2) - \ln(x+2)$
Check Domain Restrictions: Check for domain restrictions to avoid math errors. $\newline$ Calculation: $x-2$ and $x+2$ must not be zero or negative for the logarithm to be defined. $\newline$ x-2 > 0 \rightarrow x > 2 $\newline$ x+2 > 0 \rightarrow x > -2 $\newline$ Combined domain: x > 2