Problem 97 - College Algebra Essentials

Question

Evaluate or simplify each expression without using a calculator. $$e^{\ln 5 x^{2}}$$

Step-by-Step Solution

Answer

The simplified form of the expression \(e^{\ln 5x^{2}}\) is \(5x^2\).

Step 1: Recognize the relationship between \(e^x\) and \(ln x\)

These two functions are inverses of each other. That is, they undo each other. This means that for any real number x, \(e^{ln x} = x\) and \(ln(e^x) = x\). This is the property that will be primarily leveraged to simplify the given expression.

Step 2: Apply the inverse relationship

Applying the inverse relationship to the expression \(e^{ln 5x^{2}}\), we can remove the \(e\) and \(ln\), leaving us with just \(5x^2\).

Step 3: Write out the final expression

The final simplified expression will then be \(5x^2\).