Solve $e^x + e^y = 20$ for $y$

Question

I have an equation $e^x + e^y = 20$,where $e^x=\exp(x)$ and would like to express $y$ from this: $$e^y = 20 - e^x \\\ln(e^y) = \ln(20-e^x) \\ y = \frac{\ln(20)}{\ln(e^x)} \\ y =\frac{ \ln(20)}{x}.$$ Is this okay?

Answer 1

$$\ln(a-b) \ne \frac{\ln(a)}{\ln(b)}$$

Answer 2

$e^x+e^y=20$

$e^y=20-e^x$

$y=\ln(20-e^x)$

Edit:

If you really want to separate $\ln(20-e^x)$

then you can write it as $\ln(20)+\ln(1-\frac {e^x}{20})$,but that does not add any value to the result.

Answer 3

$$e^y=20-e^x$$ $$\ln(e^y)=\ln(20-e^x)$$ $$y=\ln(20-e^x)$$