Coordinates of intersection of curve and tangent line

[Guest]

I have a formula [tex]y=\frac{log(x)}{log(0.9)}[/tex] that plots as this graph


I want the coordinates of the intersection of illustrated in this rough approximation


The axes are different scales, so the line isn't actually -1 slope, it just looks that way.

How can I figure out:
1). What the slope actually is
2). The coordinates of their intersection

[Guest]

For the slope I can use [tex]\frac{dy}{dx} = \frac{-25}{0.5} = -50 slope[/tex]