Use properties of logarithms to evaluate the expression. \( \ln e^{9}-\ln e^{8}+\ln e^{6} \)

To evaluate the expression \( \ln e^{9} - \ln e^{8} + \ln e^{6} \), we can use the properties of logarithms, specifically: 1. **Power Rule of Logarithms**: \( \ln e^x = x \) because the natural logarithm (\( \ln \)) and the exponential function (\( e^x \)) are inverses of each other. Let's apply this property to each term in the expression: 1. \( \ln e^{9} = 9 \) 2. \( \ln e^{8} = 8 \) 3. \( \ln e^{6} = 6 \) Now, substitute these values back into the original expression: \[ \ln e^{9} - \ln e^{8} + \ln e^{6} = 9 - 8 + 6 = 7 \] **Final Answer:** \( 7 \)