### Related

##### logcontract

log2(x):=log(x)/log(2);

f:log2(x+1)+log2(x-5);

f:logcontract(f);

Calculate

##### logcontract-rat-ratsimpexpons-ratsubst-true

a:(x^k-1)/(2^k-1);

b:(x^k-x-1)/(2^k-2);

c: rat(b-a);

Calculate

##### logcontract

log2(x):=log(x)/log(2);

f:log2(x+1)+log2(x-5);

g:logcontract(f);

Calculate

##### logcontract

logcontract(log(y-1)-...

Calculate

##### logcontract-solve

log2(x):=log(x)/log(2);

f:log2(x+1)+log2(X-5);

g:logcontract(f);

Calculate

##### logcontract

logcontract(log(a)+lo...

Calculate

##### logcontract-solve

f:log2(x+1)+log2(x-5)=4;

g:logcontract(f);

v:solve(g=4,x);

Calculate

##### logcontract-solve

log2(x):=log(x)/log(2);

f:log2(x+1);

log2(x-5);

Calculate

##### logcontract

logcontract(log(a)+lo...

Calculate

##### logcontract-solve

log2(x):=log(x)/log(2);

f:log2(x+1)+log2(x-5);

g:logcontract(f);

Calculate

### logcontract

Run Example
```(%i1)e1: 2*(2*a*log(y)+a*log(x));
(%o1)                      2 (2 a log(y) + a log(x))
(%i2) logcontract(e1);
2  4
(%o2)                            a log(x  y )
(%i3) e2:-4*log(4)/3  + log(3)+ 2 *log(2) + 1;
4 log(4)
(%o3)                 - -------- + log(3) + 2 log(2) + 1
3
(%i4)  logcontract(e2);
4 log(4)
(%o4)                       log(12) - -------- + 1
3
(%i5) ```
Run Example
```eq1 : 'diff(P,t) = P*(a-b*P);
dP
(%o1)                          -- = P (a - b P)
dt
(%i2) gsoln : ode2(eq1, P,t), logcontract;
P
log(-------)
b P - a
(%o2)                        ------------ = t + %c
a
(%i3) gsoln : gsoln * denom(lhs(gsoln));
P
(%o3)                      log(-------) = a (t + %c)
b P - a
(%i4) gsoln : exp(lhs(gsoln)) = exp(rhs(gsoln));
P        a (t + %c)
(%o4)                       ------- = %e
b P - a
(%i5) psoln : ic1(gsoln, t=0, P=3929);
a t
P      3929 %e
(%o5)                        ------- = ----------
b P - a   3929 b - a
(%i6) ps1 : ev(psoln, t=6, P=23192);
6 a
23192      3929 %e
(%o6)                      ----------- = ----------
23192 b - a   3929 b - a
(%i7) ps2 : ev(psoln, t=12, P=91972);
12 a
91972      3929 %e
(%o7)                      ----------- = -----------
91972 b - a   3929 b - a
(%i8) ps2 : solve(ps2, b);
12 a
3929 a %e     - 91972 a
(%o8)                 [b = ----------------------------]
12 a
361357988 %e     - 361357988
(%i9) ```
Run Example
```/* SETUP DE */de : 'diff(x,t) = sin(x);
dx
(%o1)                             -- = sin(x)
dt
(%i2) sol : ode2(de,x,t);
log(cos(x) + 1) - log(cos(x) - 1)
(%o2)            - --------------------------------- = t + %c
2
(%i3) sol : logcontract(2*sol);
cos(x) - 1
(%o3)                    log(----------) = 2 t + 2 %c
cos(x) + 1
(%i4) sol : map(exp,sol);
cos(x) - 1     2 t + 2 %c
(%o4)                      ---------- = %e
cos(x) + 1
(%i5) sol : ratsubst(%A,exp(2*%c),sol);
cos(x) - 1        2 t
(%o5)                        ---------- = %A %e
cos(x) + 1
(%i6) cosx : first(solve(sol,cos(x)));
2 t
%A %e    + 1
(%o6)                       cos(x) = - ------------
2 t
%A %e    - 1
(%i7) s : first(solve(cosx,x));

solve: using arc-trig functions to get a solution.
Some solutions will be lost.
2 t
%A %e             1
(%o7)             x = %pi - acos(------------ + ------------)
2 t            2 t
%A %e    - 1   %A %e    - 1
(%i8) s : ratsimp(s);
2 t
%A %e    + 1
(%o8)                    x = %pi - acos(------------)
2 t
%A %e    - 1