Two things you learned long ago are that and that so so that sin x is approximately for x close to .

x/a= 1+ (x/a- 1) so ln(x/a) is approximately x/a- 1. That's the linearization you want.and

(b) the only fixed point for the differential equation dx/dt = ln (x/a) , a > 0.

(Hint: ln(1 + z) ~ z for |z| < 1.)

In each case verify your answer using the method of linearisation by Taylor polynomial.