Problems solving some exponentials and trig equations

Hi, 

I'm doing my final year of high school mathematics, and since I'm vision
impaired I use maxima as an accessible CAS calculator, which has worked
really well! 

However, lately I've ran into a few problems. 

1) I can not solve exponential equations simultaneously:
(%i2) solve([2=%e^(0+b)+c,6=%e^(1+b)+c],[b,c]);

(%o2) []

Attempt solve by using logs. However, it did not work. 

(%i3) solve([0+b+log(c)=log(2),log(6)=1+b+log(c)],[b,c]);

(%o3) []

2) Something a little complicated like this won't solve. 
(%i13) solve(2000*(1-%e^(-0.1*n))-20*n=0);

rat: replaced -0.1 by -1/10 = -0.1
(%o13) [n = %e^-(n/10)*(100*%e^(n/10)-100)]

3) Trig equations, some won't solve. eg. 
solve(sin(x)+cos(x)=sqrt(3)/2+1/2,x);

(%o4) [sin(x) = -(2*cos(x)-sqrt(3)-1)/2]

It also struggles with some product functions, but I think this is just
a variation of problem 2 I mentioned above:
(%i9) solve(sin(x)*%e^(x-2)=-19.260);

rat: replaced 19.26 by 963/50 = 19.26
(%o9) [sin(x) = -963*%e^(2-x)/50]

My other problem which I think I may have already asked about was
whether the solve function can solve for a given domain? And also
whether there is any way to get multiple solutions for the trig stuff?
But it seemed the answer to both those questions was no. 

Failing this and I know this probably isn't the right atitude to have,
but for the odd thing maxima can't do is there alternative software that
I could just use which would complement maxima to fill in any of the
gaps, just so I can get through my exams! :)

Any help with any of this would be greatly appreciated though.

Thank you very much. 

Dan