Problem 94 - College Algebra Essentials

Question

Evaluate or simplify each expression without using a calculator. $$e^{\ln 300}$$

Step-by-Step Solution

Answer

The simplified expression of \(e^{\ln 300}\) is 300.

Step 1: Understanding the Property of Exponentials and Logarithms

We need to apply the property that links exponentials and logarithms. The natural exponential and the natural logarithm function are inverse, or opposite, functions. This means that one function ‘undoes’ the operation of the other. In the expression \(e^{\ln x}\), the property dictates that the exponential and the natural log cancel out and the expression simplifies to just \(x\).

Step 2: Apply the Property to the Given Expression

We substitute the value of 300 for \(x\) in the equation from Step 1. This results in \(e^{\ln 300}\) simplifying to 300.