Cho alpha=logax, beta=logbx. Khi đó

* Hướng dẫn giải

Chọn C.

Ta có: ${\log }_{a{b}^2}\left(x^3\right)=3{\log }_{a{b}^2}x=\frac{3}{{\log }_x\left(a{b}^2\right)}=\frac{3}{{\log }_{x}a+2{\log }_{x}b}$

$=\frac{3}{\frac{1}{{\log }_{a}x}+\frac{2}{{\log }_{b}x}}=\frac{3{\log }_{a}x.{\log }_{b}x}{2{\log }_{a}x+{\log }_{b}x}=\frac{2\alpha \beta }{2\alpha +\beta }.$