a)
[tex] log_{a}(3) = \frac{1}{2} \\ {a}^{ \frac{1}{2} = 3 } \\ \sqrt{a} \: = 3 \\ a = 9 \: bo \: \sqrt{9} = 3[/tex]
b)
[tex] log_{a}( \sqrt{2} ) = - 1 \\ {a}^{ - 1} = \sqrt{2} \\ \frac{1}{a} \: = \frac{ \sqrt{2} }{1} \\ a \sqrt{2} = 1 \\ a \: = \frac{1}{ \sqrt{2} } \times \frac{ \sqrt{2} }{ \sqrt{2} } = \frac{ \sqrt{2} }{2} [/tex]