What is the logarithmic function modeled by the following table?
2 answers:
So we need to come up with a function that when we plug x into it, it gives us f(x). Logarithims ask: what exponent do I need to put on b (see the diagram to see what b is) to make it equal x. In the diagram below y is our f(x).
So we have logb (x) = f(x), we need to find what b is. Well the values look like 5 then 5 squared, then 5 cubed etc. So b=5.
To test this put one of the exponents (f(x)-values) on b and see if it equals the x value next to it in the table.
The answer is:
log 5 x = f(x)
So we have logb (x) = f(x), we need to find what b is. Well the values look like 5 then 5 squared, then 5 cubed etc. So b=5.
To test this put one of the exponents (f(x)-values) on b and see if it equals the x value next to it in the table.
The answer is:
log 5 x = f(x)
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Answer:
a) The x value of the point where the two equations intersect in terms of a is
b) The value of the functions at the point where they intersect is
c) The partial derivative of f with respect to is
and the partial derivative of f with respect to
is
d) The value of and
e) and
f) equation and
Step-by-step explanation:
a) In order to find the we just need to equal the equations and solve for
:
b) Since we need to find the value of the function in the intersection point we just need to substitute the result from a) in one of the functions. As a sanity check , I will do it in both and the value (in terms of ) must be the same.
and for :
c)
d) Then evaluating:
e) Substituting the corresponding values:
f) Writing the equations: