Problem 70 - College Algebra

Question

Evaluate each expression without using a calculator. $$\ln e^{7}$$

Step-by-Step Solution

Answer

The evaluated expression of \( \ln e^{7} \) is 7.

Step 1: Understanding the problem

The exercise has given the expression \( \ln e^{7} \) to evaluate. Here, \(\ln\) is the natural logarithm with base \( e \). The number \( e \) is an important mathematical constant that is the base of the natural logarithm. It is approximately equal to 2.71828.

Step 2: Applying the exponent rule of logarithms

Now, to solve this exercise, we have to remember the exponent rule of logarithms. The exponent rule of logarithms states that \(\log_{b} b^{y} = y\). Applying this rule to our problem, record that the base of our logarithm, ln, is \( e \), and we have \(\ln e^{7}\). Therefore, applying the exponent rule of logarithms gives us 7.

Step 3: Writing the final answer

According to the exponent rule of logarithm, the solution to \( \ln e^{7} \) is 7.