Create a logarithmic function to match my criteria

I need a logarithmic function that matches these criteria: The input x is between 0 and 1 The input y is also between 0 and 1, this represents 2 standard deviations (the uncertainty in x) as a percentage of x The output will be between 0 and 1. I need a logarithmic function that is flatter for higher values of y (when there is more uncertainty this will reduce the output) i.e. for this function F(x, y): F(x, 0.1) > F(x, 0.2) for all values of x. In the extreme case of 0 uncertainty, F(0,0) = 0 and F(1, 0) = 1. The curve of this function should basically follow the y=x line on a graph for 0 uncertainty, and for higher values of uncertainty it should always be under the y=x line. Please don't apply if you can't finish this within 24 hours. I need it pretty urgently.