If a = lo g_ 8\, 225 and b = lo g_ 2\, 15, then a in terms of b is -

Answer: Option B

$$\begin{array}{rl}& a={\log }_{8}225\\ & ={\log }_{2^3}\left({15}^2\right)\\ & =\frac{2}{3}{\log }_{2}15\\ & =\frac{2b}{3}\end{array}$$