Solve for x. Round to the nearest hundreth (2 decimals) 4e^2x=32 x= square

To solve the equation $4e^{2x}=32$, we can follow these steps:<br /><br />1. Divide both sides of the equation by 4 to isolate the exponential term:<br />$e^{2x}=8$<br /><br />2. Take the natural logarithm (ln) of both sides to get rid of the exponential term:<br />$2x=\ln(8)$<br /><br />3. Divide both sides by 2 to solve for x:<br />$x=\frac{\ln(8)}{2}$<br /><br />Now, we can calculate the value of x using a calculator:<br /><br />$x=\frac{\ln(8)}{2} \approx 1.40$<br /><br />Therefore, the solution to the equation $4e^{2x}=32$ is $x \approx 1.40$.