I am currently in preparations for a Math exam (BscIT) and came across some, to my current level at least, unsolvable problem.
The full function: $$f(x) = e^{-xn}(e^{-x}-7+10e^x)^n$$
The part that causes me headache is the following:
$$(e^{-x}-7+10e^x)^n = 0$$
I entered the equation into Wolfram Alpha, hit "Step by Step solution" and the output ... made me wonder...
The left hand side factors into a product with three terms
$\color{red}{-7}+e^{-x}+10e^x => e^{-x}(2e^x-1)(5e^x-1)$
Where did the $-7$ go? because this was the main issue holding me back while solving the whole mystery as regardless of how i changed everything around, i always ended up, having this horrible number somewhere, preventing me from getting a nice, simple and clean solution ...
Thanks in advance, X39
Hint: multiply out the RHS, keeping in mind that $(a+b)(c+d)=ac+ad+bc+bd$ and not $ac+bd$.