Question

expand the logarithmic expression logb square root 57/74

Answer 1

If you mean:\[\log_{b} \sqrt{\frac{ 57 }{ 74 }}=\log_{b}\left( \frac{57}{74}\right )^{\frac{1}{2}}\]you could use two rules:\[\log_{b}x^a=a \cdot \log_{b} x\]and:\[\log_{b}\frac{ p }{ q } =\log_{b}p-\log_{b}q\]

Answer 2

(In that order, btw...)