Simplify :

2 log $\dfrac{15}{8}$ - log $\dfrac{25}{162}$ + 3 log $\dfrac{4}{9}$

2 log $\dfrac{15}{8}$ - log $\dfrac{25}{162}$ + 3 log $\dfrac{4}{9}$

= 2 (log 15 - log 8) - (log 25 - log 162) + 3 (log 4 - log 9)

= 2 log 15 - 2 log 8 - log 25 + log 162 + 3 log 4 - 3 log 9

= 2 log (3 x 5) - 2 log $2^3$ - log $5^2$ + log (81 x 2) + 3 log $2^2$ - 3 log $3^2$

= 2 log 3 + 2 log 5 - 6 log 2 - 2 log 5 + log $3^4$ + log 2 + 6 log 2 - 6 log 3

= 2 log 3 + 2 log 5 - 6 log 2 - 2 log 5 + 4 log 3 + log 2 + 6 log 2 - 6 log 3

= (2 + 4 - 6)log 3 + (2 - 2)log 5 + (-6 + 1 + 6)log 2

= log 2

Hence, the value of 2 log $\dfrac{15}{8}$ - log $\dfrac{25}{162}$ + 3 log $\dfrac{4}{9}$ = log 2.