Đáp án:

 C

Giải thích các bước giải:

$\begin{split}\dfrac{2}{log_{ab}a}+\dfrac{1}{log_{\sqrt[9]{ab}}b}-log_ab&=2log_aab+log_b\sqrt[9]{ab}-log_ab\\&=2(1+log_ab)+\dfrac{1}{9}(log_bab)-log_ab\\&=2(1+log_ab)+\dfrac{1}{9}(log_ba+1)-log_ab\\&=\dfrac{19}{9}+log_ab+\dfrac{1}{9}log_ba\\&\ge \dfrac{19}{9}+2\sqrt{log_ab.\dfrac{1}{9}log_ba}\\&\ge \dfrac{19}{9}+\dfrac{2}{3}\\&=\dfrac{25}{9}\end{split}\\$ $\rightarrow \sqrt{\dfrac{2}{log_{ab}a}+\dfrac{1}{log_{\sqrt[9]{ab}}b}-log_ab}\ge \sqrt{\dfrac{25}{9}}=\dfrac{5}{3}$

Đáp án:

 C

Giải thích các bước giải:

2logaba+1log9√abb−logab=2logaab+logb9√ab−logab=2(1+logab)+19(logbab)−logab=2(1+logab)+19(logba+1)−logab=199+logab+19logba≥199+2√logab.19logba≥199+23=2592logaba+1logab9b−logab=2logaab+logbab9−logab=2(1+logab)+19(logbab)−logab=2(1+logab)+19(logba+1)−logab=199+logab+19logba≥199+2logab.19logba≥199+23=259→√logaba+1log9√abb−logab≥√259=53