1) Use properties of logarithms to evaluate the expression. \( \ln e^{15}+\ln e^{10} \)

To simplify the expression \( \ln e^{15} + \ln e^{10} \), we can use the property of logarithms that states \( \ln a^b = b \ln a \). Applying this property, we find: \[ \ln e^{15} = 15 \ln e = 15 \quad (\text{since } \ln e = 1) \] \[ \ln e^{10} = 10 \ln e = 10 \] Now, we can add these results together: \[ 15 + 10 = 25 \] So, \( \ln e^{15} + \ln e^{10} = 25 \).