# Mean reversion formula in log normal or exponential form?

The formula for the mean reversion model in log normal form:

$x=\ln(S)$

$x_{i+1} = x_i + [a(m-x_i)-\frac{1}{2}\sigma^2] dt + \sigma \sqrt{dt} \epsilon$

Can this formula be written in exponential form?

$S(i+1)= S(i)\exp([a(m-S(i))-\frac{1}{2}\sigma^2] dt + \sigma \sqrt{dt}\epsilon)$

Is there any reason why we would use the log normal form?

Thanks,

Alex