Problem 93 - College Algebra Essentials

Question

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

Step-by-Step Solution

Answer

The simplified expression is 125

Step 1: Recognize the property of natural logarithm

We firstly need to recognize that the exercise involves a property of the exponential function and the natural logarithm. In this case, the property is \(e^{\ln a} = a\), for any positive number \(a\). This comes from the fact that the natural logarithm, \(\ln(x)\), is the inverse function of the exponential function with base \(e\), \(e^x\).

Step 2: Apply the property

Now we can apply this property to the expression \(e^{\ln 125}\). Using this property, we can simplify the given expression by setting \(a = 125\) as following: \(e^{\ln 125} = 125\).