²log √6 - 1/2 ²log 3 =

[tex] log_{2}( \sqrt{6} ) - \frac{1}{2} log_{2}(3) = log_{2}( {6}^{ \frac{1}{2} } ) - \frac{1}{2} log_{2}(3) \\ = \frac{1}{2} log_{2}(6) - \frac{1}{2} log_{2}(3) \\ = \frac{1}{2} log_{2}( \frac{6}{3} ) \\ = \frac{1}{2} log_{2}(2) \\ = \frac{1}{2} [/tex]

²log √6 - 1/2 ²log 3
= ²log √6 - 1/2 ²log 3^1/2
= ²log √6 - ²log√3
= ²log √6 / ²log√3
= ²log √2
= 1/2 ²log 2
= 1/2