Making a logarithmic equation that starts at $(0,0)$ and passes through $(x, y)$?

Question

I'm writing a computer program and for fading sound, it's best to do it in a logarithmic equation. What I need it to find a graph of the "volume" that starts at (0, 0) [x is the time, y is the volume] and goes to a certain volume after a certain time, increasing based on the logarithmic graph. What's a step by step way I can compute this? (So I can translate it into code)

Sorry, I just realized my question didn't make sense. By "ends at (x, y)" I mean passes through (x, y)

Answer 1

For clarity, I'm going to change notation and say it has to pass through $(x_0,y_0)$. Then we can start with $f(x) = A \, ln(x+1)$, which is logarithmic and passes through $(0,0)$. We need $y_0 = A \, ln (x_0+1)$, so we have $A = \frac{y_0}{ln(x_0+1)}$. So the answer is $f(x) = \frac{y_0}{ln(x_0+1)} \, ln(x+1)$.