Exponential equation with negative base with rational solution

[sylee957]

I see exponential equation solving is not implemented for rationals for negative or complex bases

from sympy import *

x = Symbol('x')

a = (-2*I)**2
b = (-2*I)**3

solveset(a**x - b, x, S.Rationals)

But it should be improved to give the solutions satisfying the diophantine problem like below

from sympy import *

n1, n2 = symbols('n1 n2', integer=True)

a = (-2*I)**2
b = (-2*I)**3
ratio = simplify(log(abs(a)) / log(abs(b)))
assert ratio.is_Rational
p, q = ratio.p, ratio.q

angle_a = cancel(arg(a) / pi)
angle_b = cancel(arg(b) / pi)
assert angle_a.is_Rational
assert angle_b.is_Rational

eqn = q*(2*n1 + angle_a) - p*(2*n2 + angle_b)
eqn = Poly(eqn, n1, n2)
coeff_n1 = eqn.coeff_monomial(n1)
coeff_n2 = eqn.coeff_monomial(n2)
coeff_const = eqn.coeff_monomial([0, 0])

_, _, gcd = gcdex(coeff_n1, coeff_n2)
assert (coeff_const % gcd) == 0
print(1/ratio)