Clarification of one-way property of hash functions One-way property: computationally infeasible to find data mapping to
  specific hash


The definition above is a little vague, if we have h(x) = floor(log(x)), finding "some" x that gives a hash value is easy, however, deterministically finding the actual x value that has led to the output is impossible. Do such hash functions have the one-way property?
Your function is too easy. Given an hash value $h$, calculate $b^h$ and $b^{h+1}-1$, where b is the base of your logarithm.

Any value between $b^h$ and $b^{h+1}-1$ will be pre-image.