Log linearising (Gali textbook)
$$\frac{x_{t+1}}{x_t} \equiv \frac{x_{t}+Δx_{t+1}}{x_t} = 1+\frac{Δx_{t+1}}{x_t}$$

Further,

$$\ln (1+a) \approx a,$$

an acceptable approximation for $|a| &lt;0.1$ and certainly for $|a| &lt;0.05$.