MHB Find value of X in this equation

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The discussion centers on finding the value of x in the equations f(x)=5+2x and g(x)=2^x, specifically under the condition that f'g(x)=3/2. Participants clarify that f' refers to the derivative of f, leading to the interpretation that f'(x)g(x) must equal 3/2. The confusion arises from the notation, with suggestions to clarify whether the composition of functions or the product of the derivative and function value is intended.

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

-Dan
 

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