Chapter 5 - Exponential and Logarithmic Functions - 5.6 Logarithmic and Exponential Equations - 5.6 Assess Your Understanding - Page 311: 38

$1+\sqrt[3] 2\approx2.260$

Step 1. Rewrite the equation as $log(x-1)=log(\sqrt[3] 2)$ Step 2. Thus $x-1=\sqrt[3] 2 \longrightarrow x=1+\sqrt[3] 2$. Step 3. Check answers, $x=1+\sqrt[3] 2\approx2.260$ fits the original equation.