Chapter 4 - Exponential and Logarithmic Functions - Section 4.6 Logarithmic and Exponential Equations - 4.6 Assess Your Understanding - Page 337: 40

$e, e^4 $

1. Treat $\sqrt {ln(x)}$ as a single unit, $ln(x)-3\sqrt {ln(x)}+2=0 \Longrightarrow (\sqrt {ln(x)})^2-3\sqrt {ln(x)}+2=0 \Longrightarrow (\sqrt {ln(x)}-1)(\sqrt {ln(x)}-2)=0 \Longrightarrow \sqrt {ln(x)}=1,2 \Longrightarrow ln(x)=1,4 \Longrightarrow x=e, e^4 $. 2. Check $x=e, e^4 $ fit(s).