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?

  • 4
    $\begingroup$ I've rolled back to your initial suggested solution, because otherwise it looks weird if the answers are identical to the question. $\endgroup$ – Arnaud D. Apr 10 '18 at 12:03
  • $\begingroup$ that's fine @ArnaudD. $\endgroup$ – mandella Apr 10 '18 at 12:07

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

  • $\begingroup$ oh, I made a mistake there. Is there any way to separate this? $\endgroup$ – mandella Apr 10 '18 at 11:21
  • $\begingroup$ see edit in my answer $\endgroup$ – The Integrator Apr 10 '18 at 11:29





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.

  • $\begingroup$ thank you, I just fixed it $\endgroup$ – mandella Apr 10 '18 at 11:22

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


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