How to find logarithmic function when only given its features?

Question

I'm not sure how to go about doing this. You don't have to answer it, but explain how I can do it.. somehow.. Thanks!!

A graph has the following key features:

Decreasing for x > 0
y-intercept of 1
No x-intercept
A horizontal asymptote of y = 0
Domain: {x|xER}
Range:{y|y > 0, yER}
(1, 0.5) is a point of the graph

A possible function with these key features is....

Answer 1

Well, maybe it's in the form a + b*ln(cx).

b is obviously positive and c is obviously negative.

Given the horizontal asymptote, a has to be zero.

You know two points on the graph, so each gives an equation in b and c. And I think you'll find that pair of equations pretty easy to solve. ;)