sage: log(8,-2)
3*log(2)/(I*pi + log(2))

sage: 8.log(-2)
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Cell In[2], line 1
----> 1 Integer(8).log(-Integer(2))

File ~/SAGE_ROOT/src/sage/rings/integer.pyx:2861, in sage.rings.integer.Integer.log()
   2859 cdef int self_sgn
   2860 if m is not None and m <= 0:
-> 2861     raise ValueError("log base must be positive")
   2862 self_sgn = mpz_sgn(self.value)
   2863 if self_sgn < 0 and prec is None:

ValueError: log base must be positive

sage: (8.0).log(-2.0)
0.139260970636224 - 0.631180872623791*I

------------------------------------------------------------------------------------[Another Example]--------------------------------------------------------------------------------------------

sage: log(8,0)
0

sage: 8.log(0)
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Cell In[10], line 1
----> 1 Integer(8).log(Integer(0))

File ~/SAGE_ROOT/src/sage/rings/integer.pyx:2861, in sage.rings.integer.Integer.log()
   2859 cdef int self_sgn
   2860 if m is not None and m <= 0:
-> 2861     raise ValueError("log base must be positive")
   2862 self_sgn = mpz_sgn(self.value)
   2863 if self_sgn < 0 and prec is None:

ValueError: log base must be positive

sage: (8.0).log(0.0)
-0.000000000000000