Chapter 5 - Exponential and Logarithmic Functions - 5.6 Logarithmic and Exponential Equations - 5.6 Assess Your Understanding - Page 311: 40

$e, e^4$

Step 1. Let $u=\sqrt {ln\ x}$, rewrite the equation as $u^2-3u+2=0 \longrightarrow (u-1)(u-2)=0 \longrightarrow u=1,2$ Step 2. For $u=1$, we have $\sqrt {ln\ x}=1 \longrightarrow x=e$. Step 3. For $u=2$, we have $\sqrt {ln\ x}=2 \longrightarrow ln\ x=4 \longrightarrow x=e^4$. Step 4. Check answers, $x=e, e^4$ fit the original equation.