Chapter 4 - Exponential and Logarithmic Functions - Section 4.6 Logarithmic and Exponential Equations - 4.6 Assess Your Understanding - Page 337: 36

$(2)^{\frac{7}{3}}$

1. $3(log_7(x)-log_7(2))=2log_7(4) \Longrightarrow log_7(x)-log_7(2)=\frac{2}{3}log_7(4) \Longrightarrow log_7(x)=log_7(2)^{\frac{4}{3}}+log_7(2)=log_7(2)^{\frac{7}{3}} \Longrightarrow x=(2)^{\frac{7}{3}}$. 2. Check only $x=(2)^{\frac{7}{3}}$ fits.