Is there any way to simplify the following expression for $x$?
$$ 0=\ln(ae^{bx} + ce^{dx}) $$
Thank you.
Asked
Active
Viewed 37 times
0
-
You can exponentiate both sides to get $1 = ae^{bx} + ce^{dx}$. – Dan May 27 '22 at 19:52
-
Simplify or Solve ? – Claude Leibovici May 28 '22 at 03:11
-
@layabout That is irrelevant because $ae^{bx}+ce^{dx}$ is not the same as $e^x(ae^b+ce^d)$. – anon May 28 '22 at 04:43
-
For what purpose, OP? You will not be able to solve that in general using elementary functions. You can write it as a series using Newton-Mercator though. And maybe there are some other polarization tricks that might be helpful. Depends on what the actual goal here is. – anon May 28 '22 at 04:46
-
Solve the expression for $x$, not simplify. I'm assuming I'm out of luck. – pythoner May 28 '22 at 17:32
-
If $a$ and $c$ are opposite signs and not too small, and $b$ and $d$ are large enough, then the solution to $ae^{bx}+ce^{dx}=1$ approximately equals the solution to $ae^{bx}+ce^{dx}=0$, which you should be able to solve. You still haven't said why you're trying to solve this equation, though. It's possible you arrived at this equation after working on some other problem which we can help with, or show you how it could have led somewhere other than this equation. – anon May 28 '22 at 19:09