Find the value of a so that the tangent line to y = ln(x) at x = a is a line through the origin.

Question

I am unsure how to go about this.

Answer 1

the slope of the tangent line at x=a is 1/a.

If the line goes through the origin, its equation is

y = kx.

Clearly, at x=e, the line through (e,1) has slope 1/e.

So, a=e

see

http://www.wolframalpha.com/input/?i=plot+y%3Dlnx%2C+y+%3D+1%2Fe+x