Cho a, b là...

A

- Hướng dẫn giải

Đáp án A

Ta có: $P={\log }_{\sqrt{ab}}\frac{b}{\sqrt{a}}=2{\log }_{ab}\frac{b}{\sqrt{a}}$

$=2\left({\log }_{ab}b-{\log }_{ab}\sqrt{a}\right)=2\left(\frac{1}{{\log }_{b}ab}-\frac{1}{2}{\log }_{ab}a\right)$

$$\begin{gathered} =2\left(\frac{1}{1+{\log }_{b}a}-\frac{1}{2}.\frac{1}{{\log }_{a}ab}\right) \\ =2\left(\frac{1}{1+\frac{1}{{\log }_{a}b}}-\frac{1}{2}.\frac{1}{1+{\log }_{a}b}\right) \\ =2\left(\frac{1}{1+\frac{1}{\sqrt{5}}}-\frac{1}{2}.\frac{1}{1+\sqrt{5}}\right)=\frac{11-3\sqrt{5}}{4} \end{gathered}$$