Logarithmic equation, solving w/ limits of 2 variables: Y(x) = a*t(x) / ln (b/c-w(x))

[lo9999s]

Hello everyone, I've come across a problem I'm not quite able to solve and I would be very thankful if someone here could give me a hand.
I have the following equation:

Y(x) = a*t(x) / ln (b/c-w(x))

a, b and c are constants, and w varies over time.
My first problem is that I come across undefined values.
The term c - w(x) decreases over time until it reaches the value 0, which is of course a problem, since log(0) doesn't exist.
Next issue is that the term b/(c-w(x) at the very beginning has the value 1, and log(1) is 0, which makes my denominator zero and of course division by zero is also not possible.
I know that I have got to define values, but I am not sure where to start with.

My constant values are:
a= 0.25
b=0.5
c=14.3

t(x) has values starting from 0 until 178,
c(x) has values starting from 13.8 until 14.3

If anyone can give me a hint on how this is better solved I would really appreciate it!

Thanks a lot for taking the time to read this!

 

[Dr.Peterson]

Hello everyone, I've come across a problem I'm not quite able to solve and I would be very thankful if someone here could give me a hand.
I have the following equation:

Y(x) = a*t(x) / ln (b/c-w(x))

a, b and c are constants, and w varies over time.
My first problem is that I come across undefined values.
The term c - w(x) decreases over time until it reaches the value 0, which is of course a problem, since log(0) doesn't exist.
Next issue is that the term b/(c-w(x) at the very beginning has the value 1, and log(1) is 0, which makes my denominator zero and of course division by zero is also not possible.
I know that I have got to define values, but I am not sure where to start with.

My constant values are:
a= 0.25
b=0.5
c=14.3

t(x) has values starting from 0 until 178,
c(x) has values starting from 13.8 until 14.3

If anyone can give me a hint on how this is better solved I would really appreciate it!

Thanks a lot for taking the time to read this!

How are you using the word "solve"? It isn't clear what your goal is, but I don't think you're actually solving an equation to find x.

Are you asking what the graph will look like? Are you thinking that this function is not properly defined, and want to change it to something else? Or do you just want to know what the limits are at x=0 and w(x) = c, so you can "evaluate" Y(x) in those cases by using the limits, if they exist?

If the function is defined for a good reason (because it represents some real behavior), then what happens at those points may still represent real behavior! What do you expect that to be?

There are a couple specific problems with what you've said, that we'll have to clear up:

Since you mention "c - w(x)" as an entity, you must have omitted parentheses around it. But since when it is zero, you would be dividing b by 0, not taking ln(0), something more is wrong here. And I imagine where you described c(x), you meant w(x).

For a first check, I would temporarily replace t(x) and w(x) with linear functions so you have a specific example you can graph, and run it through a grapher to see what it looks like. That may answer your questions. I won't try that myself until I'm sure of the function. I'm taking it for the moment to be Y(x) = a*t(x) / ln(b/(c-w(x))), i.e.
\(\displaystyle \displaystyle Y(x) = \frac{a \cdot t(x)}{ln \left( \frac{b}{c-w(x)}\right)}\)