Content
The function f is defined by f(x)=log3(x+1). Triangle △OPQ is drawn under the graph of y=f(x) where O is the origin, P has a y-coordinate of 1, and the triangle is right angled at Q.
Powered by Desmos
Find
The coordinates of P.
To earn a crown, get your answer ready before you reveal the options!
The ratio [OQ][PQ]
A second triangle, △PRS, is drawn such that △PRS and △OPQ are similar, S lies on the curve of y=f(x), and R=(r,0), where r>2.
A line L is drawn passing through the points P and R.
Show that L has the equation y=2−rx−r.
Show that the x-coordinate of S is r+2.
By considering the slope of RS, show that 2log3(r+3)=r−2.
Hence find the value of r.
Ask Plex AI about this problem
Get hints, ask questions, and work through this problem step by step