If log x - log (2x - 1) = 1, the value of x is :

1. $\dfrac{19}{10}$

2. 19 × 10

3. $\dfrac{10}{19}$

4. $\dfrac{1}{19 \times 10}$

Given,

$\Rightarrow \text{log } x - \text{log } (2x - 1) = 1 \\[1em] \Rightarrow \text{log } \dfrac{x}{2x - 1} = \text{log } 10 \\[1em] \Rightarrow \dfrac{x}{2x - 1} = 10 \\[1em] \Rightarrow x = 10(2x - 1) \\[1em] \Rightarrow x = 20x - 10 \\[1em] \Rightarrow 20x - x = 10 \\[1em] \Rightarrow 19x = 10 \\[1em] \Rightarrow x = \dfrac{10}{19}.$

Hence, Option 3 is the correct option.