Question 1153723: Write a logarithmic equation
Use
f(x) = log5(x)
as the parent function. Ordered pair (-3,-2)
y =
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
We can have function(s) of the form
Given that the function is to have an integer value at x=-3, we want -3+b to be a power of 5.
(a) first example
5^0 = 1; -3+b = 1 --> b = 4
We want the function value at -3 to be -2, so we need to subtract 2. Our first function that satisfies the requirements is
A graph (window -10 to 10; -5 to 2):
(b) second example
5^1 = 5; -3+b = 5 --> b = 8
We want the function value at -3 to be -2, so we need to subtract 3. Our second function that satisfies the requirements is
A graph (window -10 to 10; -5 to 2), showing both graphs passing through (-3,-2):
We can also have functions of the form
Again using b=8,
We want the function value to be -2 at x=-3; so we can multiply this function by -2. Our third function that satisfies the requirements is
A graph again, showing the graphs of all three functions passing through (-3,-2):
You should be able to see that we can get as many functions as we want that satisfy the requirement.
Here is one more that gives the value -2 at x=-3:
One more graph, showing all four functions passing through (-3,-2):
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