Rút gọn biểu thức P=1-log^3a(b)/(loga(b)+logb(a)+1)loga(a/b)

* Hướng dẫn giải

Ta có 

$$\begin{gathered} P=\frac{1-{{\log }^3}_a\left(b\right)}{\left({\log }_a\left(b\right)+{\log }_b\left(a\right)+1\right){\log }_a\left({\displaystyle \frac{a}{b}}\right)} \\ =\frac{\left(1-{\log }_a\left(b\right)\right)\left(1+{{\log }^2}_a\left(b\right)+{\log }_a\left(b\right)\right)}{\left({{\log }^2}_a\left(b\right)+1+{\log }_a\left(b\right)\right)} \\ ={\log }_a\left(b\right) \end{gathered}$$

Đáp án B