Chapter 3.1, Problem 52E

To determine

To find: The value of $x$ .

Answer to Problem 52E

  $x=\frac{5}{2}$ .

Explanation of Solution

Given information:

An exponential equation is given as $e^{2x-1}=e^4$

Concepts used:

One-to-one property:

If $e^x=e^y,\text{then }x=y$ .

Calculation:

Given exponential equation is $e^{2x-1}=e^4$ .

Using one-to-one property,

  $\begin{array}{l}{e}^{2x-1}=e^4\\ \Rightarrow 2x-1=4\\ \Rightarrow 2x=4+1\\ \Rightarrow 2x=5\\ \Rightarrow x=\frac{5}{2}\end{array}$

Hence, simplified value is $x=\frac{5}{2}$ .