Chapter 4 - Exponential and Logarithmic Functions - Section 4.6 Logarithmic and Exponential Equations - 4.6 Assess Your Understanding - Page 338: 89

$-1, \frac{2}{3}$

1. $(\sqrt[3] 2)^{2-x}=2^{x^2} \Longrightarrow \frac{2-x}{3}\ ln2=x^2\ ln2 \Longrightarrow 3x^2+x-2=0 \Longrightarrow (3x-2)(x+1)=0 \Longrightarrow x=-1, \frac{2}{3}$ 2. Check, $x=-1, \frac{2}{3}$ fit(s).