Can someone help in reversing this equation?

Question

I have Tf1(ADC1), but need to find out ADC1

Answer 1

Let $f = Tf_{1}$, let $x = ACD_{1}$

We have $$f(x) = \frac{9}{\frac{\ln(\frac{c}{x}-\frac{1}{5})}{676}+d}-459.67$$

with $c = 207.08502024291497975584, d= 0.016770082173402649673$

$$(\frac{\ln(\frac{c}{x}-\frac{1}{5})}{676}+d)f(x) = 9 - 459.67(\frac{\ln(\frac{c}{x}-\frac{1}{5})}{676}+d)$$

$$(f(x)+459.67)(\frac{\ln(\frac{c}{x}-\frac{1}{5})}{676})= 9 -459.67d -df(x)$$

$$\frac{\ln(\frac{c}{x}-\frac{1}{5})}{676} = \frac{ 9 -459.67d -df(x)}{f(x)+459.67}$$

$$\frac{c}{x}-\frac{1}{5} = e^{ \frac{676( 9 -459.67d -df(x))}{f(x)+459.67}}$$

$$\frac{c}{x} = \frac{5e^{ \frac{676( 9 -459.67d -df(x))}{f(x)+459.67}}+1}{5}$$

$$x = \frac{5c}{5e^{ \frac{676( 9 -459.67d -df(x))}{f(x)+459.67}}+1}$$