\(\frac{1}{3}\left(2x-\frac{1}{2}\right)^4=\frac{1}{243}\)
=> \(\left(2x-\frac{1}{2}\right)^4=\frac{1}{243}:\frac{1}{3}=\frac{1}{243}\cdot3=\frac{1}{81}\)
=> \(\left(2x-\frac{1}{2}\right)^4=\left(\pm\frac{1}{3}\right)^4\)
=> \(\hept{\begin{cases}2x-\frac{1}{2}=\frac{1}{3}\\2x-\frac{1}{2}=-\frac{1}{3}\end{cases}}\Rightarrow\hept{\begin{cases}x=\frac{5}{12}\\x=\frac{1}{12}\end{cases}}\)
(2x-1/2)^4=1/243:1/3
(2x-1/2)=1/243×3/1
(2x-1/2)^4=1/81
(2x-1/2)^4=1/3^4
(2x-1/2)=1/3
2x=1/3+1/2
2x=5/6
x=5/6:2/1
x=5/6×1/2
x=5/12