1)) Use properties of logarithms to evaluate the expression. $$ \ln e^{12}-\ln e^{8} $$

Question

UpStudy AI · Accepted Answer

1. Start with the expression:
   $$
   \ln e^{12} - \ln e^{8}
   $$

2. Use the logarithmic property that $$\ln e^x = x$$:
   $$
   \ln e^{12} = 12 \quad \text{and} \quad \ln e^{8} = 8
   $$

3. Substitute these into the original expression:
   $$
   12 - 8
   $$

4. Simplify the result:
   $$
   4
   $$

Thus, the evaluated expression is $$4$$.
The expression evaluates to 4.

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