Question

At what point do the graphs of y=log_5 x and y=log_0.5x intersect

Answer 1

Solve ln x / ln 5 = ln x / ln(0.5). Rearranging gives ln x (ln 0.5 − ln 5) = 0. Since ln 0.5 ≠ ln 5, we must have ln x = 0, so x = 1. Then y = log_5(1) = 0.

They intersect at (1, 0).