Maxima Cheat Sheet

Maximas solve cannot handle exponential equations. However, it converts them into a form which can be used further by taking the logarithm of both sides. Make sure to set 'logexpand' to 'all':

f(x):=a*2^((x-2)/2)+2;
g(x):=b*3^((x-4)/5)+1;
solve(f(x)=g(x),x);
                                         x - 4
                              x - 2      -----
                              -----        5
                                2     b 3      - 1
(%o8)                       [2      = ------------]
                                           a
 
logexpand:all;
solve(log(solve(f(x)=g(x),x)),x);
                            x/5 - 4/5
                   2 log(b 3          - 1) - 2 log(a) + 2 log(2)
(%o11)        [x = ---------------------------------------------]
                                      log(2)