The value of in terms C of B is C = g(x)/log₅(x) - [f(x) - Bln(x)]/Blog₅(x)
What is the value of in terms C of A?
From the question, we have the following parameters that can be used in our computation:
f(x) = AB + Bln(x)
g(x) = A + Clog₅(x)
From the first equation, we have
AB = f(x) - Bln(x)
So, we have
A = [f(x) - Bln(x)]/B
Recall that
g(x) = A + Clog₅(x)
So, we have
g(x) = [f(x) - Bln(x)]/B + Clog₅(x)
This gives
Clog₅(x) = g(x) - [f(x) - Bln(x)]/B
Divide through by log₅(x)
C = g(x)/log₅(x) - [f(x) - Bln(x)]/Blog₅(x)
Hence, the value of in terms C of B is C = g(x)/log₅(x) - [f(x) - Bln(x)]/Blog₅(x)
Question
A regression is calculated on a data set of coordinate pairs (x, y). The resulting regression model is f(x) = AB + Bln(x) , where A > 0 and B > 1.
The same model can be expressed as g(x) = A + Clog₅(x) . What is the value of in terms C of B?