Econ 407 : Solution to the bonus question

> Qd:=120.0-8*log(p);

Qd := 120.0-8*ln(p)

> Qs:=50*log(p)-60;

Qs := 50*ln(p)-60

> solve(Qd=Qs,p);

22.27462807

> eval(Qd, p=22.27462807);

95.17241379

> log[10](1268.96);

3.103447933

> Qd:=120.0-(8)*log[10](1268.96);

Qd := 95.17241654

> solve(120.0-(8)*log[10](p)=(50.0)*log[10](p)-60.0,p);

-1261.522299-137.1988181*I   -1261.522299+137.1988181*I   -1202.534919-405.1811900*I   -1202.534919+405.1811900*I   -1087.318342-654.2177398*I   -1087.318342+654.2177398*I   -921.2599677-872.6637952*I   -921.2599677+872.6637952*I   -712.1245014-1050.305061*I   -712.1245014+1050.305061*I   -469.6908849-1178.835230*I   -469.6908849+1178.835230*I   -205.2950446-1252.244374*I   -205.2950446+1252.244374*I   68.70016375-1267.099963*I   68.70016375+1267.099963*I   339.4830288-1222.707365*I   339.4830288+1222.707365*I   594.3920448-1121.142330*I   594.3920448+1121.142330*I   821.5079494-967.1539261*I   821.5079494+967.1539261*I   1010.211055-767.9424792*I   1010.211055+767.9424792*I   1151.677815-532.8228955*I   1151.677815+532.8228955*I   1239.293400-272.7891055*I   1239.293400+272.7891055*I   1268.961003

>

Note that of all the soulutions, only the last one is a real solution-- the rest have an imaginery part. We only accept the last soulution.