Abuzer,
> solve(log(0.25*(2*b+5)) - 0.5*log(5*b-5),b);
Solve cannot handle this case directly, however, you can solve the
equation easily and exactly using Maxima:
expr: log(0.25*(2*b+5)) - 0.5*log(5*b-5);
Enter expression
expr1: fullratsimp(expr) => (2*log((2*b+5)/4)-log(5*b-5))/2
Convert decimals to exact fractions
expr2: logcontract(expr1) => -log((80*b-80)/(4*b^2+20*b+25))/2
Combine the logarithms
solve(expr2,b) => [b = -(2*sqrt(30)-15)/2,b = (2*sqrt(30)+15)/2]
Of course, you can evaluate the results numerically if you like.
-s