$${\dfrac{x-5}{x} = \left(\dfrac{5}{x}\right)^\sqrt{2x+2}}$$
So at the first glance, I thought maybe this was a normal equation and that can be easily solved using logarithm. I was wrong... (after hours of trying).
There are two (possible) ideas which I think possible to solve this problem:
- Try to solve $x$ for which, $$0 = \frac {d}{dx} | lhs - rhs |$$I was thinking that the functional graph must be at the minimum if $x$ is the right answer for the equation.
- Brute-force all possible real numbers (using computer programming to do this job).
However, I'm also thinking that it must have other ways to solve for $x$ which I have no skills/knowledge whatsoever in order to solve the equation.
This is not my homework, it's just random challenge that popped out while I'm surfing the net!