[latex]=log[10^{1/2}]^{1/3}-log[(10^{2})^{1/3}]^{1/2}=log10^{1/6}-log10^{1/3}=1/6-1/3\=1/6-2/6=-1/6[/latex]

[latex]\log(10^ frac{1}{2} )^ frac{1}{3} -log(10^ frac{2}{3} )^ frac{1}{2} =log(10 ^frac{1}{6} :10^ frac{1}{3} )=log10^{- frac{1}{6}} =- dfrac{1}{6} [/latex]