Chapter 5 - Exponential and Logarithmic Functions - 5.6 Logarithmic and Exponential Equations - 5.6 Assess Your Understanding - Page 311: 11

$x=16$

We know that $\log_a {x^n}=n\cdot \log_a {x}$, hence the equation $\frac{1}{2}\log_3{x}=2\log_3{2}$ becomes $\log_3{x^{\frac{1}{2}}}=\log_3{2^2}.$ RECALL: $\log_a{b}=\log_a{c} \longrightarrow b=c$ Hence, $\log_3{x^{\frac{1}{2}}}=\log_3{2^2}\longrightarrow x^{\frac{1}{2}}=2^2$. Solve the equation above to obtain \begin{align*} x^{\frac{1}{2}}&=2^2\\ x^{\frac{1}{2}}&=4\\ \ \left(x^{\frac{1}{2}}\right)^2&=4^2\\ x&=16 \end{align*}