No, Ratish….it needs to be consistently definable across the entire “domain of definition. We would find difficulty defining, say, log (-4) to base (-2) and so on. Possibly the more esoteric branches of maths would have ways around this (using complex numbers, possibly) but as far as we are concerned, a log should not be defined for a negative number or to a negative base.
CAT-holics 
Would log of a negative number to a negative base be correct? For example, log (-8) to the base (-2) would be 3.
No, Ratish….it needs to be consistently definable across the entire “domain of definition. We would find difficulty defining, say, log (-4) to base (-2) and so on. Possibly the more esoteric branches of maths would have ways around this (using complex numbers, possibly) but as far as we are concerned, a log should not be defined for a negative number or to a negative base.
regards
J
i had the same doubt!