Chapter 4 - Exponential and Logarithmic Functions - Section 4.6 Logarithmic and Exponential Equations - 4.6 Assess Your Understanding - Page 338: 88

$\frac{1}{16}, 4$

1. $2(log_{4}(x))^2+3log_8(x)=log_216 \Longrightarrow 2(\frac{log(x)}{2log2})^2+3(\frac{log(x)}{3log2})=4 \Longrightarrow (log_2(x))^2+2log_2(x)-8=0 \Longrightarrow log_2(x)=-4,2 \Longrightarrow x=\frac{1}{16}, 4$ 2. Check, $x=\frac{1}{16}, 4$ fit(s).