Question

Find a point such that the tangent line to ln x at (a, ln a) crosses the origin.

Answer 1

so we have two point (a,lna) and origin that is (0,0)

Answer 2

so use slope point formula

Answer 3

\[y-0=\frac{ lna-0 }{ a-0 }(x-0)\]

Answer 4

\[y=\frac{ \ln a }{ a }x\]