Chapter 4 - Exponential and Logarithmic Functions - Section 4.6 Logarithmic and Exponential Equations - 4.6 Assess Your Understanding - Page 337: 39

$\frac{1}{3}, 729$

1. Treat $log_3(x)$ as a single unit, $(log_3(x))^2-5(log_3(x))=6 \Longrightarrow (log_3(x))^2-5(log_3(x))-6=0 \Longrightarrow (log_3(x)+1)(log_3(x)-6)=0 \Longrightarrow log_3(x)=-1,6 \Longrightarrow x=\frac{1}{3}, 729$. 2. Check $x=\frac{1}{3}, 729$ fit(s).