Biết rằng

C

- Hướng dẫn giải

Đáp án C

Ta có:  ${\log }_{25}56=\frac{1}{2}{\log }_{5}56=\frac{1}{2}{\log }_5\left(2^3.7\right)=\frac{1}{2}\left(3.{\log }_{5}2+{\log }_{5}7\right).$

Mà ${\log }_{5}100=2{\log }_{5}10=2\left(1+{\log }_{5}2\right)=b\Rightarrow {\log }_{5}2=\frac{b}{2}-1$ và $\log 7.{\log }_{5}10={\log }_{5}7=\frac{ab}{2}.$ 

Vậy  ${\log }_{25}56=\frac{1}{2}\left[3.\left(\frac{b}{2}-1\right)+\frac{ab}{2}\right]=\frac{ab+3b-6}{4}.$