Answer:
x= +i and x = -i
Explanation:
First we use the property of a sum of logarithms (the sum of two logarithms is equal to multiplying them) and we have that
log (x) + log (-x) = 0
log((x)(-x)) = 0
log (-x²) = 0
we can write this as an exponential equation. ( When you have a single logarithm on one side of the equation then you can express it as an exponential equation and solve)
-x²= 10⁰
-x²= 1
x²= -1
x= ±i
Therefore the solutions are x= +i and x = -i