Sorry for not clarifying properly!
Basically what I'm saying is that if the common ratio is negative, the power essentially determines the parity of the term ie. whether it is odd or even. Say we had a geometric sequence with first term 1, and common ratio -0.5 - it'd go something like this: 1, -0.5, 0.25, -0.125, 0.0625... and so on. Note that for every odd term, the power on top of the common ratio in the formula ar
n-1 is odd: for the second term, -0.5, we have (1)(-0.5)
2-1.
Note also, that \((ab)^n=a^n \times b^n\); this means that essentially, if we have any negative number to an odd power, we can split them up to form -1 to that same odd number, and the absolute value of that number to that same power. ie. (-a)
n = (-1)
n x a
n.
Remembering that -1 to any odd power is just -1, and combining this with the first paragraph, we essentially just stick a minus out the front and leave the common ratio positive for odd powers ie. negative terms - ie. we can just remove them all together, since both sides are negative. Then you can just perform a logarithm as usual.
It's a similar case for a positive number/even power, because we have -1 to an even power, and that is just 1; there are in actuality no negative signs to even contend with, so you can just do a log anyway.
Hope this helps