If x = log $\dfrac{3}{5}, \text{ y = log } \dfrac{5}{4}\text{ and z = 2 log } \dfrac{\sqrt{3}}{2}$, the value of x + y - z is :

1. 1

2. -1

3. 2

4. 0

Solving,

$\Rightarrow x + y - z = \text{log } \dfrac{3}{5} + \text{log } \dfrac{5}{4} - \text{ 2 log } \dfrac{\sqrt{3}}{2} \\[1em] = \text{log } \dfrac{3}{5} + \text{log } \dfrac{5}{4} - \text{log } \Big(\dfrac{\sqrt{3}}{2}\Big)^2 \\[1em] = \text{log } \dfrac{3}{5} + \text{log } \dfrac{5}{4} - \text{log } \dfrac{3}{4} \\[1em] = \text{log } \dfrac{\dfrac{3}{5} \times \dfrac{5}{4}}{\dfrac{3}{4}} \\[1em] = \text{log } \dfrac{\dfrac{3}{4}}{\dfrac{3}{4}} \\[1em] = \text{log } 1 \\[1em] = 0.$

Hence, Option 4 is the correct option.