On 28/10/2012 11:22 AM, David Billinghurst wrote:
> On 28/10/2012 9:59 AM, Daniel Dalton wrote:
>> 3. I have two integrals, which must equal 3 and 2 respectively. So I
>> assign the integrated equation to f(x) in maxima and attempt to solve
>> for the two integrals like this simultaneously:
>> f(x):=7*log(x);
>>
>> (%o3) f(x):=7*log(x)
>> (%i4) solve([f(m*n)-f(1)=3, f(m/n)-f(1)=2],[m,n]);
>> (%o4) []
>>
>> How do I find the solution to this? (I need an exact value)
> Here is one approach. I use map to apply exp() to each side of the
> equations
> You could then use solve directly, but there are 49 solutions and only
> one has real roots.
>
> (%i1) display2d:false$
> (%i2) f(x):=7*log(x)$
> (%i3) eq1:f(m*n)-f(1)=3;
> (%o3) 7*log(m*n) = 3
> (%i4) eq2:f(m/n)-f(1)=2;
> (%o4) 7*log(m/n) = 2
> (%i5) eq3:map(exp,eq1);
> (%o5) m^7*n^7 = %e^3
> (%i6) eq4:map(exp,eq2);
> (%o6) m^7/n^7 = %e^2
>
> (%i10) eq5:solve(eq4,n^7);
> (%o10) [n^7 = %e^-2*m^7]
>
> (%i12) eq6:eq3,eq5;
> (%o12) %e^-2*m^14 = %e^3
> (%i13) solve(eq6,m);
> (%o13) [m = %e^(%i*%pi/7+5/14),m = %e^(2*%i*%pi/7+5/14),
> m = %e^(3*%i*%pi/7+5/14),m = %e^(4*%i*%pi/7+5/14),
> m = %e^(5*%i*%pi/7+5/14),m = %e^(6*%i*%pi/7+5/14),m = -%e^(5/14),
> m = %e^(5/14-6*%i*%pi/7),m = %e^(5/14-5*%i*%pi/7),
> m = %e^(5/14-4*%i*%pi/7),m = %e^(5/14-3*%i*%pi/7),
> m = %e^(5/14-2*%i*%pi/7),m = %e^(5/14-%i*%pi/7),m = %e^(5/14)]
>
> (%i14) eq7:eq5,m = %e^(5/14);
> (%o14) [n^7 = sqrt(%e)]
> (%i15) solve(%,n);
> (%o15) [n = %e^(2*%i*%pi/7+1/14),n = %e^(4*%i*%pi/7+1/14),
> n = %e^(6*%i*%pi/7+1/14),n = %e^(1/14-6*%i*%pi/7),
> n = %e^(1/14-4*%i*%pi/7),n = %e^(1/14-2*%i*%pi/7),n = %e^(1/14)]
>
... and also the other real solution
(%i17) eq5,m = -%e^(5/14);
(%o17) [n^7 = -sqrt(%e)]
(%i18) solve(%,n);
(%o18) [n = -%e^(2*%i*%pi/7+1/14),n = -%e^(4*%i*%pi/7+1/14),
n = -%e^(6*%i*%pi/7+1/14),n = -%e^(1/14-6*%i*%pi/7),
n = -%e^(1/14-4*%i*%pi/7),n = -%e^(1/14-2*%i*%pi/7),n = -%e^(1/14)]