\(log\dfrac{1}{2}+log\dfrac{2}{3}+...+log\dfrac{149}{150}=log\left(\dfrac{1.2...149}{2.3...150}\right)=log\dfrac{1}{150}=-log150\)
\(\Rightarrow I=\dfrac{log150}{log126}=\dfrac{log_2150}{log_2126}=\dfrac{1+log_23+2log_25}{1+2log_23+log_27}\)
\(log_25=\dfrac{log_35}{log_32}=log_35.log_23=ac\)
\(\Rightarrow I=\dfrac{1+c+2ac}{1+2c+b}\)