[latex]1) frac{lg4}{lg64-lg8} [/latex] [latex]2) log_{ frac{8}{27} } frac{81}{16} [/latex] [latex]3) 5^{-6 log_{5}2} [/latex]

[latex]1)frac{lg4}{lg64-lg8}=frac{lg4}{lgfrac{64}8}=frac{lg4}{lg8}=log_84=log_{2^3}2^2=frac{2}3\\2)log_frac{8}{27}frac{81}{16}=-log_frac{8}{27}frac{16}{81}=-log_{(frac{2}3)^3}(frac{2}3)^4=-frac{4}3\\3)5^{-6log_52}=frac{1}{5^{log_52^6}}=frac{1}{2^{6log_55}}=frac{1}{2^6}=frac{1}{64}[/latex]