Chapter 5 - Exponential and Logarithmic Functions - 5.6 Logarithmic and Exponential Equations - 5.6 Assess Your Understanding - Page 312: 87

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

Step 1. Take logarithm on both sides $(2-x)ln(\sqrt[3] 2)=x^2ln2 \longrightarrow (2-x)ln(2)=3x^2ln2 \longrightarrow 3x^2+x-2=0 \longrightarrow (3x-2)(x+1)=0 \longrightarrow x=-1, \frac{2}{3}$ Step 2. Check, $x=-1, \frac{2}{3}$ fit the original equation.