Question 218334
*[Tex \LARGE \log_{6}\left(\sqrt{6}\right)=\log_{6}\left(6^{\frac{1}{2}\right)=\frac{1}{2}\log_{6}\left(6\right)=\frac{1}{2}(1)=\frac{1}{2}]



So *[Tex \LARGE \log_{6}\left(\sqrt{6}\right)=\frac{1}{2}]



In this problem, I used the following identities: 



1) *[Tex \LARGE \sqrt{x}=x^{\frac{1}{2}}]



2) *[Tex \LARGE \log_{b}\left(x^y\right)=y\log_{b}\left(x\right)]



3) *[Tex \LARGE \log_{b}\left(b\right)=1]



note: {{{b>1}}}