U) Use properties of logarithms to evaluate the expression. In \( e^{12}-\ln e^{8} \)

Let’s break this down into manageable parts. The term \( e^{12} \) is simply equal to \( e^{12} \) since we don't have to simplify it further. However, when we look at \( \ln e^{8} \), we can apply the property of logarithms that states \( \ln a^b = b \cdot \ln a \). Here, we have \( \ln e^{8} = 8 \cdot \ln e \). Since \( \ln e = 1 \), it follows that \( \ln e^{8} = 8 \). Now, substituting back into the expression, we have \( e^{12} - 8 \). Voilà! To evaluate, you would write it as it is: \( e^{12} - 8 \). This is a straightforward evaluation that combines exponential and logarithmic properties seamlessly!