Question 947531
Choose the base you want.  Base ten is used here.


{{{log(10,y)=log(10,(ab^x))}}}
{{{log(10,y)=log(10,a)+x*log(10,b)}}}
{{{highlight(log(10,y)=x*log(10,b)+log(10,a))}}}
This equation is now in linear form.


The given points need to be reprocessed to fit with the linear formed equation.  The vertical axis coordinates must be  {{{log(10,45)}}}  and {{{log(10,1215)}}}.


The slope of the line is  {{{highlight_green(log(10,b)=(log(10,1215)-log(10,45))/(5-2))}}}.
Solve for b.


Slope-intercept form will still be convenient to use for find the vertical axis INTERCEPT.  Recall {{{f=mx+v}}};
If v is for vertical axis intercept, f for the vertical axis value at any x,
{{{v=f-mx}}}.
Choose either of your treated points which fit the linearized equation, the now found slope, and solve for the value of your vertical axis intercept.