Question

Show that $\frac{\log \sqrt{27}+\log 8+\log \sqrt{1000}}{\log 120}=\frac{3}{2}$

Answer 1

$\frac{\log \sqrt{27}+\log 8+log\sqrt{1000}}{\log 120}=\frac{\frac{3}{2}\times \log 3+\frac{3}{2}\times \log 4+\frac{3}{2}\times \log 10}{\log 120}$

$=\frac{\frac{3}{2}\times \log 120}{\log 120}$

$=\frac{3}{2}$