Chapter 12, Problem 3CR

To determine

The solution of equation $2e^x=5$.

Answer to Problem 3CR

Solution:

The solution set of the equation $2e^x=5$ is $\left\{\ln \left(\frac{5}{2}\right)\right\}$.

Explanation of Solution

Given information:

The equation, $2e^x=5$

Explanation:

To solve the given equation multiply both sides by $\frac{1}{2}$,

$\Rightarrow e^x=\frac{5}{2}$

Taking natural logarithm of both sides,

$\Rightarrow \ln \left(e^x\right)=\ln \left(\frac{5}{2}\right)$

$\Rightarrow x=\ln \left(\frac{5}{2}\right)\approx 0.916$

Therefore, the solution set of the equation $2e^x=5$ is $\left\{\ln \left(\frac{5}{2}\right)\right\}$.