Find value of X in this equation

[aruwin]

Hi, everyone.
Can someone guide me in finding the value of x in this equation?
I have left calculus for a very long time and I came across this question and wanted to try but I have forgotten a lot of things.
f(x)=5+2x and g(x)=2^x

Find the possible value of x such that f'g(x)=3/2

 

[Evgeny.Makarov]

Find the possible value of x such that f'g(x)=3/2

It depends on what you denote by $f'g(x)$. Usually $f'$ denotes the derivative of $f$; in this case $f'g(x)$ means the derivative of $f$ multiplied by the value of $g$ at $x$. However, it is not clear at what value $f'$ is taken. If it said $f'(x)g(x)$, then there would be no questions.

The second option is that you mean the composition of $f$ and $g$, which is usually denoted by $(f\circ g)(x)$. Could you say what you mean?

 

[topsquark]

f'(g(x)) = 3/2 is impossible, so I'm assuming it's f'(x) g(x).

-Dan