SOLUTION: what is the logarithmic function that passes through the points (18,4) and (144,10).

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: what is the logarithmic function that passes through the points (18,4) and (144,10).       Log On


   

Question 1061136: what is the logarithmic function that passes through the points (18,4) and (144,10).

Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Description specified, "logarithmic" function.

Choose your base, maybe 10.
Let m be the slope for the LINE, but you would start with a line such as y=m%2Alog%28%28x%29%29%2Blog%28%28k%29%29.

The format comes from rules for logarithms which can take the equation back to y=log%28%28x%5Em%29%29%2Blog%28%28k%29%29
y=log%28%28k%29%29%2Blog%28%28x%5Em%29%29
highlight_green%28y=log%28%28k%2Ax%5Em%29%29%29------to this.


The two given points give this system:


You might work with the system in this arrangement:



Solve the system for these: system%28m%2Cand%2Clog%28%28k%29%29%29.


Choosing to eliminate log%28%28k%29%29 with the Elimination Method will give highlight%28m=6.6439%29.
Using the log(144) & 10 equation, find log%28%28k%29%29=-4.33985, and that highlight%28k=4.572%2A10%5E%28-5%29%29.


(REMEMBER, all of this is being done for base-ten):
Your logarithmic formula or FUNCTION f, is highlight%28f%28x%29=log%28%28%280.00004572%29x%5E6.6439%29%29%29.