Chapter 12 - Section 12.8 - Exponential and Logarithmic Equations and Problem Solving - Exercise Set - Page 896: 17

{$\frac{1}{2}$}

$\log_{4} 2+\log_{4} x=0$ $\log_{4} (2\times x)=0$ $\log_{4} (2x)=0$ $2x=4^{0}$ $2x=1$ $x=\frac{1}{2}$ Checking the answer by inserting it in $\log_{4} (2x)=0$: $\log_{4} (2\times\frac{1}{2})=0$ $\log_{4} (1)=0$ $\log_{4} 4^{0}=0$ $0\log_{4} 4=0$ $0=0$ Therefore, the solution set is {$\frac{1}{2}$}.