Question 1061136
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*log((x))+log((k))}}}.


The format comes from rules for logarithms which can take the equation back to {{{y=log((x^m))+log((k))}}}
{{{y=log((k))+log((x^m))}}}
{{{highlight_green(y=log((k*x^m)))}}}------to this.



The two given points give this system:
{{{system(4=m*log((18))+log((k)),10=m*log((144))+log((k)))}}}


You might work with the system in this arrangement:
{{{system(m*log((18))+log((k))=4,m*log((144))+log((k))=10)}}}



Solve the system for these:   {{{system(m,and,log((k)))}}}.



Choosing to eliminate {{{log((k))}}} with the Elimination Method will give {{{highlight(m=6.6439)}}}.

Using the log(144) & 10 equation, find {{{log((k))=-4.33985}}}, and that {{{highlight(k=4.572*10^(-5))}}}.



(REMEMBER, all of this is being done for base-ten):
Your logarithmic formula or FUNCTION f, is  {{{highlight(f(x)=log(((0.00004572)x^6.6439)))}}}.