Cho \({\log _{14}}7 = a,\,{\log _{14}}5 = b\). Tính \({\log _{35}}28\) theo a, b.

Cho \({\log _{14}}7 = a,\,{\log _{14}}5 = b\). Tính \({\log _{35}}28\) theo a, b.
A. \({\log _{35}}28 = \frac{{1 - a}}{{a - b}}\)
B. \({\log _{35}}28 = \frac{{2 - a}}{{a + b}}\)
C. \({\log _{35}}28 = \frac{{2 + a}}{{a - b}}\)
D. \({\log _{35}}28 = \frac{{1 - a}}{{a + b}}\)

\(\begin{array}{l} {\log _{35}}28 = \frac{{{{\log }_{14}}28}}{{{{\log }_{14}}35}} = \frac{{{{\log }_{14}}14.2}}{{{{\log }_{14}}7 + {{\log }_{14}}5}}\\ = \frac{{{{\log }_{14}}14.\frac{{14}}{7}}}{{{{\log }_{14}}7 + {{\log }_{14}}5}} = \frac{{{{\log }_{14}}{{14}^2} - {{\log }_{14}}7}}{{{{\log }_{14}}7 + {{\log }_{14}}5}} = \frac{{2 - a}}{{a + b}} \end{array}\)