MATLAB: Solve a nonlinear equation

Question

Hi, Could you please help me to solve this equation in terms of "q"

1.082 [ (q-1) log((3/4 -3q/4)/(1-3q/4))+ q*log((3q/4) *(3/4 -3q/4)] + 1.4427[-3log(1-q/2) *((q/2)  -1)+(q/2+1/2)^2 *log(q/2+1/2)- (3q/4 -1)*log(1-3q/4)- (3q/4+1/4)*log(3q/4+1/4)] + 0.7213[q*log(q/2)* ( -q-3/2 +1/q)+ (-q-1)*log(q/2 +1/2) + q*(-q/2+1/2)*log(1/2-q/2)-3*log(1-q/2)-(q-1)*log(1/2 - q/2)] -0.36 *[(q-1)^2*log(1/2 - q/2)]=0

Answer 1

If you assume natural logs, then there are no non-complex solutions.

The value of the expression (assuming natural logs) is negative between 0 and 1 (going to negative infinity at those two bounds.) Outside of that range, the expression is real-valued at exactly one point near -3.000138648 and at exactly one point near 1.851008154. At those two exceptional locations, the expression has positive non-zero values. The fact that there are negative values and positive values does not, however, imply that there are points at which the function is real-valued and 0, as the function is discontinuous.

The results have the same shape if log10 is used instead of ln.