If $${\text{a}} = {\text{lo}}{{\text{g}}_{\text{8}}}\,{\text{225}}$$   and $${\text{b = lo}}{{\text{g}}_{\text{2}}}\,{\text{15}},$$   then a in terms of b is -

A. $$\frac{b}{2}$$

B. $$\frac{{2b}}{3}$$

C. b

D. $$\frac{{3b}}{2}$$

Answer: Option B

Solution(By Examveda Team)

$$\eqalign{ & a = {\log _8}225 \cr & = {\log _{{2^3}}}\left( {{{15}^2}} \right) \cr & = \frac{2}{3}{\log _2}15 \cr & = \frac{{2b}}{3} \cr} $$