Chapter 8, Problem 10PT

To determine

To find: The solution of the given equation.

Answer to Problem 10PT

The solution of the given equation is $x=0.2027$

Explanation of Solution

Given:

The given equation is,

  $4e^{2x}-1=5$

Calculation:

Solve the given equation.

  $\begin{array}{l}4e^{2x}-1=5\\ 4e^{2x}=5+1\\ 4e^{2x}=6\\ e^{2x}=1.5\end{array}$

Solve further as,

  $\begin{array}{l}\ln e^{2x}=\ln 1.5\\ 2x=0.404\\ x=0.2027\end{array}$

Thus, the solution of the given equation is $x=0.2027$