Problem 89 - College Algebra Essentials

Question

Evaluate or simplify each expression without using a calculator. $$\ln e^{6}$$

Step-by-Step Solution

Answer

After simplifying the expression \(\ln e^{6}\), we find that it equals \(6\).

Step 1: Recall the property of logarithms

The essential property of natural logarithms to recall here is that \(\ln(e^x) = x\). The argument of the logarithm function \(e^x\) simplifies directly to \(x\). This property is very useful when working with logarithmic expressions involving the base \(e\).

Step 2: Apply the Property to the Expression

We can apply the property mentioned above to the expression \(\ln e^{6}\). According to the rule, this simplifies directly to \(6\).