No, an ln function by itself is always equal to or greater than 0. Have a look at a graph for ln(x), you'll see it squashes right up against the y axis but never actually crosses it. This is because when you take a log, you're looking for the power to which you must raise the base of your logarithm to get the number in the brackets. Put more clearly:
loga(b) = c if ac = b. ln(x) = loge(x), so if your b is negative, you're asking for the power to which you can raise e to get a negative number. Since e is positive, it doesn't matter what power you raise it to, it's always gonna be positive.
