Logarithmic equation, solving with limits of 2 variables

[Guest]

Hello everybody!

I have come across a problem I'm not able to solve.
On the picture attached you can see my equation.
I'm trying to solve for v(t) which stands for volume. My volume varies over time. My equation consists of 3 constants (a, b and c). T(time) in the numerator varies as well from the starting value 0 until the end value of 178.
C(t), is a variable (current) which also values over time and has values starting from 13.8 until 14.3.

My problems are the following:

1. The term c-d(t) tends to zero. (starts at 0.5 and ends at 0). This results in a division by zero, which of course i can't work with.
2. The term inside the ln (b/c-d(t) starts with the value 1. Ln(1)=0 which again ends up in division by zero.

I know I've got to define limits in order to solve this equation since there are some values my equation cannot take due to the logarithm, but I'm not quite sure how to start, since I have too many variables in my equation.

If anyone could give me a hand with this I would really appreciate it.

Thanks a lot for your time!

[Guest]

There is NO "C(t)" in what you post. Did you mean "d(t)"? How is "d(t)" defined? You say, I think, that d(0)= 13.8. How do you know that?