Problem 73 - College Algebra

Question

Evaluate each expression without using a calculator. $$e^{\ln 125}$$

Step-by-Step Solution

Answer

So the evaluation of the given expression \(e^{\ln 125}\) is 125.

Step 1: Understand the Problem

We are given the expression \(e^{\ln 125}\) and we need to recognize that we can use the property of logarithms that \(e^{\ln a} = a\), which will greatly simplify the task.

Step 2: Apply Logarithmic Property

We can now apply this property to our given expression. This principle states that any number (a) raised to the natural logarithm of another number is simply that other number. Meaning, \(e^{\ln 125} = 125\).

Step 3: Write the Final Answer

After applying the property, we found that \(e^{\ln 125}\) simply simplifies to 125.