I understand what you mean, but the problem is that the terminology has a precisely defined meaning, and if you ignore the convention you will be misunderstood. It would be like saying that a certain O(log n) algorithm has an exponential complexity -- the meaning is completely different. The growth of a function concerns the dependent variable, so y=e^x has exponential growth, while y=ln(x) is logarithmic. See also:

http://en.wikipedia.org/wiki/Logarithmic_growth

http://en.wikipedia.org/wiki/Exponential_growth

(Sorry for the off-topic tangent!)