Good catch. The "C"s in the right side of the last two equations should be lower case (ideally, all the lower case "c"s should be subscripted). Those were typos. I have edited my original post to reflect this. My results and yours now match.
Some braces are missing in my equations because I copied and pasted William's equation.
I have edited my original post to reflect these corrections.
To get log to the base x:
[latex]log_xz = \frac{log(z)}{log(x)}[/latex]
It doesn't matter whether you use log to the base e or to the base 10 for this.
You've tested for equality, but my point was if 1-(V/Vc) is positive (negative) at any instant, also Vc/(Vc-V) is positive (negative) at the same instant because it's the reciprocal.
Len's equation seems correct to me. I got it from Roff's equation applying the formula ln(1/x) = -1*ln(x)
You've tested for equality, but my point was if 1-(V/Vc) is positive (negative) at any instant, also Vc/(Vc-V) is positive (negative) at the same instant because it's the reciprocal.
Len's equation seems correct to me. I got it from Roff's equation applying the formula ln(1/x) = -1*ln(x)