Chapter 5 - Exponential and Logarithmic Functions - 5.6 Logarithmic and Exponential Equations - 5.6 Assess Your Understanding - Page 311: 36

$2^{7/3}\approx5.040$

Step 1. Rewrite the equation as $log_{7}(x)=\frac{2}{3}log_{7}(4)+log_{7}(2) \longrightarrow log_{7}(x)=log_{7}(2^{4/3}2)$ Step 2. Thus $ x=2^{7/3}$. Step 3. Check answers, $x=2^{7/3}\approx5.040$ fits the original equation.