Question

E hoir giúp c của e, nhờ thầy Lâm trả lời giúp e ạ 

Answer 1

\(log_x\left(x^2y^3\right)=log_xx^2+log_xy^3=2+3log_xy\)

\(\Rightarrow2+3log_xy=1\Rightarrow log_xy=-\dfrac{1}{3}\)

\(N=\dfrac{log_x\left(x^2y^3\right)}{log_x\left(\dfrac{\sqrt[5]{x^3y^2}}{xy^3}\right)}=\dfrac{1}{log_x\left(\sqrt[5]{x^3y^2}\right)-log_xxy^3}=\dfrac{1}{log_x\sqrt[5]{x^3}+log_x\sqrt[5]{y^2}-\left(log_xx+log_xy^3\right)}\)

\(=\dfrac{1}{\dfrac{3}{5}+\dfrac{2}{5}log_xy-\left(1+3log_xy\right)}=\dfrac{1}{\dfrac{3}{5}+\dfrac{2}{5}.\left(-\dfrac{1}{3}\right)-1-3.\left(-\dfrac{1}{3}\right)}=\dfrac{15}{7}\)