Question

Tính giá trị của biểu thức :

          \(B=\log_{3-2\sqrt{2}}\left(27^{\log_92}+2^{\log_827}\right)\)

 

 

Answer 1

\(F=\log_{3-2\sqrt{2}}\left(27^{\log_92}+2^{\log_827}\right)=\log_{3-2\sqrt{2}}\left[\left(3^3\right)^{^{\log_92^2}}+2^{\log_{2^3}3^3}\right]\)

   \(=\log_{3-2\sqrt{2}}\left(3^{\frac{3}{2}\log_32}+2^{\log_23}\right)\)

   \(=\log_{3-2\sqrt{2}}\left(3^{\log_32^{\frac{3}{2}}}+2^{\log_23}\right)\)

   \(=\log_{3-2\sqrt{2}}\left(2^{\frac{3}{2}}+3\right)=\log_{\left(3-2\sqrt{2}\right)^{-1}}\left(3-2\sqrt{2}\right)=-1\)