Check the syntax: Solve
does not take Assumptions
, you give them with the equation itself. What values of a,b,c
did you use? With a = 2, b = 4, y = 2
I get no solution:
With[{a = 2, b = 4, y = 2},
Solve[y == 2^c a (4 + 4 (a/b)^(3/c))^(-c/3), c, Reals]]
With[{a = 2, y = 2, b = 4},
Plot[y - 2^c a (4 + 4 (a/b)^(3/c))^(-c/3), {c, -4, 4}]]
Reduce
gives False
:
Reduce[y == 2^c a (4 + 4 (a/b)^(3/c))^(-c/3) && a < y < b && a > 0 &&
b > 0, c, Reals]
Anyway, with respect to c
the equation is tascendental, very unlikely to have a symbolic solution with symbolic coefficients.