Question

Express in term of $\log 2$ and $\log 3$:
(i)$\log 4.5$
(ii) $\log \frac{26}{51}-\log \frac{91}{119}$

Answer 1

(i)$\log 4.5=\log \frac{9}{2}=\log 9-\log 2=\log 3^2-\log 2=2\log 3-\log 2$
(ii)$\log \frac{26}{51}-\log \frac{91}{119}=\log (\frac{26}{51}\cdot \frac{119}{91})=\log (\frac{2\cdot 13}{3\cdot 17}\cdot \frac{7\cdot 17}{7\cdot 13})=\log \frac{2}{3}=\log 2-\log 3$