Correct option is ((B) 1.5
\(\frac{log\sqrt{27}+log\,8-\,log\,\sqrt{1000}}{log\,1.2}\)
\(=\frac{log\,3^\frac32+log\,2^3-\,log\,10^\frac32}{log\,1.2}\)
\(=\frac{\frac32\,log\,3+3\,log\,2-\frac32\,log\,10}{log\,1.2}\)
\(=\frac{\frac32\,(log\,3+\,log\,2^2-\,log\,10)}{log\,1.2}\)
\(=\frac{\frac32\,log\,(\frac{3\times4}{10})}{log\,1.2}\) \(=\frac32\,\frac{log\,(1.2)}{log\,(1.2)}\)
\(=\frac32=1.5\)
