Problem 69 - College Algebra

Question

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

Step-by-Step Solution

Answer

The value of the expression \(\ln e^{6}\) is 6.

Step 1: Understand the problem

The problem involves evaluating the natural logarithm of an exponent of Euler's number. Since the base of the natural logarithm is 'e', it simplifies the problem.

Step 2: Using the property of logarithms

The property of logarithms says that \(\ln (e^n)=n\), where 'n' is any real number. This is because 'e' is the base of the natural logarithm.

Step 3: Applying the property to the given problem

In this problem, \(n=6\). Substitute '6' for 'n' in the log property. So, \(\ln (e^6) = 6\).