So I'm trying to solve a system of equations and I checked some other guys solution and he divides the function by the derivate, like so: $f(x)/f'(x)$.
Find the values of the real constant $k$ for which this holds true:
$$
\log(2x) \leq kx \leq e^{x/2}, \quad x > 0
$$
I convert this into 2 systems of equations:
$$
f(x)=\log(2x)=kx \ and \ f'(x)=1/x=k \\
f(x)=e^{x/2}=kx \ and \ f'(x)=\frac{e^{x/2}}{2}=k
$$
Then I got stuck,checked some other guys solution and he did this: $f(x)/f'(x)$ for both equations. Why?
Sorry for the long winded explanation but I really can't figure out why it's $f(x)/f'(x)$.
Progress
Figured it out. Dividing $f(x)$ with $f'(x)$ is just another way of creating an expression for x and inserting it into the other equation in the system.
that guy
obtained a correct answer by an incorrect method. $\endgroup$