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)]